The thrust of 1 Peter 2:13-3:7 seems to be about living differently in existing relationships "for the Lord's sake" because we have been changed - note 2:13 "for the Lord's sake...", 3:1 "in the same way...", and 3:7 "in the same way...". Why muddy the waters by referring to the wife as weaker? In what sense does he mean "weaker"?
Don't confuse 'mud' with the Biblical view of man and woman: patriarchal; by institution of God. But more specifically, 'the weaker vessel' in first century context is most likely referring to, by way of analogy, things like glass jars and so forth: so more honor to the wife just as you give more care to more brittle vessels, e.g. glass (e.g. cf. 2 Tim 2:20). That is, if anything, they are more precious, not of less worth or dignity (cf. 1 Pet 3:4b)! I recall that even in the 6th century Arabian/Eastern culture, this was still a metaphor used (Sahih al-Bukhari 6202).
Exceptions (by definition) aside, women are certainly more delicate physically, and from experience personally, often more delicate natured in general. If we treated women the same as men, that is, as if oblivious to the differences between the sexes, the world would look like... well, look at the trend of the world right now.
The modern world has a phobia for any innate, constitutional, complimentary differences in the sexes, which, if we are to understand the Bible, needs to be left behind as the worthless intellectual novelty it is.
I really believe this verse is simply saying this and nothing deeper: women being the weaker sex, take good care of your wives.
Is it 'ageist' to say 'take good care of your kids?' No. Is it 'sexist' to say 'take good care of your wife?' No.
St. Peter is saying the equivalent of what a decreasing number of people today would agree with: 'women and children first!' Why? Well if you can't ascertain some reasons, are you even trying to think realistically, or just inventing equality where it doesn't exist (e.g. equality of physical ability)?
The modern world says 'treat everyone as if they were equal in every way.' Which is irrational and actually careless advice. The Biblical view is, 'No, treat people as they are in fact, but with equal dignity as images of God.' This is telling the truth. The former is a form of lies.
Peter enjoins the brethren to behave considerately toward the "cisterns". That is, he tells them to live with them "according to knowledge" with regard to their being more fragile and with less strength. Note that he appeals to the physical situation rather than to roles. This being the case it may often be the case that the woman is the stronger and more robust and in that case it would be appropriate for the woman to bear the brunt rather than the man.
Who should change the oil in the car? Peter is saying that the believer is to use their brains to decide the question. The obvious answer for the thinking man is "Jiffy Lube". But if that is not an option, then you ask, should it be the husband or the wife? Again, for the thinking man the answer is easy: neither, it should be the teenage son. But he's away at Cobbler School. The teenage daughter? No, she might break a nail. And so on until finally the man has to say, "Okay, I'll do it". But sometimes the wife is the more physically capable and should be the one to do the chore. Yes, Peter's message is that simple. Use the right tool for the job. The man is generally stronger and less vulnerable and should therefore normally be the tool to use for jobs requiring strength or causing wear and tear.
I had always understood σκεῦος as a "jar" with the wife being the more fragile jar but the word is more general than that and can refer to any kind of "tool", including a man's penis (scroll to the right to see the highlighted text):
σκεῦος, ους, τό (Aristoph., Thu.+) ① a material object used to meet some need in an occupation or other responsibility, gener. thing, object used for any purpose at all (e.g. a table: Diod S 17, 66, 5) Mk 11:16 (PCasey, CBQ 59, ’97, 306–32). σκεῦος ἐλεφάντινον or ἐκ ξύλου Rv 18:12ab. Pl. (Diod S 13, 12, 6) Dg 2:2–4. Of all one has (Jos., Vi. 68; 69) τὰ σκεύη αὐτοῦ his property Lk 17:31.—Mt 12:29; Mk 3:27 (both in allusion to Is 49:24f).—By an added statement or via the context σκ. can become an object of a certain specific kind: τὰ σκεύη τῆς λειτουργίας the equipment used in cultic service Hb 9:21 (ParJer 3:9; 11:18; cp. Jos., Bell. 6, 389 τὰ πρὸς τὰς ἱερουργίας σκεύη). Also τὰ ἅγια σκεύη Ox 840, 14; 21; 29f (Jos., Bell. 2, 321; cp. Plut., Mor. 812b σκεῦος ἱερόν; Philo, Mos. 2, 94; Just., D. 52, 3 σκεύη ἱερά). τὸ σκεῦος Ac 27:17 seems to be the kedge or driving-anchor (Breusing 17ff; Blass and Haenchen ad loc.; Voigt [s. σκευή]. Differently HBalmer, Die Romfahrt des Ap. Pls 1905, 355ff. See FBrannigan, TGl 25, ’33, 182–84; PEdg 6 [=Sb 6712], 10 [258 B.C.] ἄνευ τῶν ἀναγκαίων σκευῶν πλεῖν τὰ πλοῖα. Pl. also X., Oec. 8, 11f; ; TestJob 18:7 and elsewh. of ship’s gear; Arrian, Peripl. 5, 2 τὰ σκεύη τὰ ναυτικά. Eng. tr. have ‘gear’, ‘sails’). Ac 10:11, 16; 11:5 represent a transitional stage on the way to 2. ② a container of any kind, vessel, jar, dish, etc. (Aristoph., Thesm. 402; X., Mem. 1, 7, 5; Aelian, VH 12, 8; Herodian 6, 7, 7; LXX; Jos., Ant. 7, 106; 8, 89; PsSol 17:38; TestNapth 2:2; JosAs; Just., A I, 9, 2 ἐξ ἀτίμων … σκευῶν) Lk 8:16; J 19:29; 2 Ti 2:20 (four kinds as Plut., Caes. 730 [48, 7]). τὸ κενὸν σκεῦος Hm 11:13. ποιεῖν σκ. make a vessel 2 Cl 8:2. τὰ σκεύη τὰ κεραμικά Rv 2:27 (s. κεραμικός). σκ. εἰς τιμήν or εἰς ἀτιμίαν (s. τιμή 2b) Ro 9:21; 2 Ti 2:21 (a fig. sense makes itself felt in the latter pass.). ③ a human being exercising a function, instrument, vessel fig. ext. of 1 or 2 (Polyb. 13, 5, 7 Δαμοκλῆς ὑπηρετικὸν ἦν σ.) for Christ Paul is a σκεῦος ἐκλογῆς a chosen instrument Ac 9:15.—Of the body, in which the Spirit dwells (cp. TestNapht 8:6 ὁ διάβολος οἰκειοῦται αὐτὸν ὡς ἴδιον σκεῦος; ApcMos 16 γενοῦ μοι σκεῦος; and the magical prayer in FPradel, Griech. u. südital. Gebete1907, p. 9, 11f ἐξορκίζω σε ἐξελθεῖν ἀπὸ τοῦ σκεύους τούτου) Hm 5, 1, 2. Christ’s body as τὸ σκ. τοῦ πνεύματος the vessel of the Spirit B 7:3; 11:9; cp. τὸ καλὸν σκεῦος 21:8 (of the human body, as ApcSed 11:5 [p. 134, 17 Ja.] ὦ χεῖρες … διʼ ἃς τὸ σκεῦος τρέφεται; cp. 10 [ln. 25 Ja.]; 11 [ln. 27 Ja.]). On the human body as ὀστράκινα σκεύη 2 Cor 4:7, s. ὀστράκινος. Those who are lost are σκεύη ὁργῆς Ro 9:22 p 928 (cp. Jer 27:25.—CDodd, JTS 5, ’54, 247f: instruments of judgment; sim. AHanson, JTS 32, ’81, 433–43), those who are saved σκ. ἐλέους vs. 23.—1 Pt 3:7 woman is called ἀσθενέστερον σκεῦος (ἀσθενής 2a). τὸ ἑαυτοῦ σκεῦος 1 Th 4:4 from antiquity has been interpreted to mean one’s own body (Theodoret, Calvin, Milligan, Schlatter, MDibelius; RKnox, transl. ’44; CCD transl. ’41, mg.; NRSV) or one’s own wife (Theodore of Mopsuestia, Schmiedel, vDobschütz, Frame, Oepke; WVogel, ThBl 13, ’34, 83–85; RSV et al.). The former interpr. is supported by passages cited at the beg. of this section 3, and the latter is in accord w. rabb. usage (Billerb. III 632f. S. also κτάομαι 1). **Also probable for 1 Th 4:4 is ‘penis’ (so Antistius [I A.D.] in Anthol. Plan. 4, 243; Aelian, NA 17, 11; cp. the euphemistic Lat. ‘vasa’ in this sense: Plautus, Poenulus. 863; s. MPoole, Synopsis Criticorum Ali. Sacrae Script., rev. ed.1694, V col. 908; on sim. usage at Qumran s. TElgvin, NTS 43, ’97, 604–19; NAB  renders guarding his member [difft. rev. ed. of NAB, 1986]. Cp. KDonfried, NTS 31, ’85, 342). In such case κτᾶσθαι must mean someth. like ‘gain control of’, etc.—DELG. M-M. EDNT. TW.** Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., pp. 927–928). Chicago: University of Chicago Press.
1Th 4:3 For this is the will of God, even your sanctification, that ye should abstain from fornication: 1Th 4:4 That every one of you should know how to possess his vessel [σκεῦος] in sanctification and honour; 1Th 4:5 Not in the lust of concupiscence, even as the Gentiles which know not God:
So men, when there is a job to do that requires a stronger, tougher tool then call Jiffy Lube. Or step up. Unless your woman is the stronger, tougher tool. Use your brains; and your sensitive caring heart. If you lack a sensitive caring heart, watch a few episodes of Oprah, I guess, or read 1 Peter 3:7.
Peter's use of 'weaker' is not intended to 'muddy the waters' - his words unintentionally reflect the prevailing male perspective in society at the time: that women were assumed to be inherently more fragile or 'weaker', both physically and emotionally. He's mistaken in this, of course, just as his support of a servant-master relationship is outdated and we are no longer ruled by an emperor. But we shouldn't throw the baby out with the bath water, so to speak.
Most of us now understand that 'weakness' is a matter of perspective, that not all women are the same, and that these types of gross generalisations and uneven power relationships are oppressive to say the least. It took almost another two thousand years to get to this stage, mind you, so I think we can forgive Peter for not yet seeing it this way, or at least for writing to these communities within their own cultural and historical discourse.
Peter's intention becomes clearer when we consider it is to this piece of text that Peter refers when he writes "in the same way..."
Be subject for the Lord’s sake to every human institution, whether it be to the emperor as supreme, or to governors as sent by him to punish those who do wrong and to praise those who do right. For it is God’s will that by doing right you should put to silence the ignorance of foolish men. Live as free men, yet without using your freedom as a pretext for evil; but live as servants of God. Honor all men. Love the brotherhood. Fear God. Honor the emperor.
Servants, be submissive to your masters with all respect, not only to the kind and gentle but also to the overbearing. For one is approved if, mindful of God, he endures pain while suffering unjustly. For what credit is it, if when you do wrong and are beaten for it you take it patiently? But if when you do right and suffer for it you take it patiently, you have God’s approval. For to this you have been called, because Christ also suffered for you, leaving you an example, that you should follow in his steps. He committed no sin; no guile was found on his lips. When he was reviled, he did not revile in return; when he suffered, he did not threaten; but he trusted to him who judges justly. 1 Peter 2:13-25
Here Peter warns against the use of violence, protest or righteous indignation - we are not expected to be revolutionaries, to overturn governments or subvert authorities. Jesus' example was to turn the other cheek when persecuted, even when he had done nothing wrong.
Peter also makes it clear that he does not advocate abandoning our legal obligations in these relationships, and instead assures us that we can and should live as Jesus intended while continuing to fulfil our duties to master, wife or husband to the highest standards as expected in our contemporary society.
So Peter 3:1-6 is not a call for women to return to submissiveness, but to continue to be to your husband what is expected these days of a 'good' wife, by honouring the vows you made and treating him with due honour and respect as your husband in today's society.
Likewise Peter 3:7 is not a call to treat your wife as 'the weaker vessel', but to continue to fulfil your vows to her, and to treat her with all due respect and honour as your wife.