The Hebrew word מַשָּׂא (massa) literally means "burden"; however, in Hebrew idiom it also meant the "weight/burden" of a message to be proclaimed. Ellicott has this comment:
(33) The burden of the Lord.—The English expresses the literal meaning
of the word, “something lifted up, or borne.” It passed, however, as
the English equivalent has done, through many shades of meaning, and
became, in the language of the prophets, one of the received terms for
a solemn, emphatic utterance. In 1Chronicles 15:22; 1Chronicles 15:27
it is applied to the chanted music of the Temple. Isaiah had brought
it into use (see Note on Isaiah 13:1), and employs it twelve times as
the title of special prophecies. Jeremiah never uses it of his own
messages, probably, as this verse indicates, because it had become a
favourite formula with the false prophets. This seems a more rational
view than that which assumes that the false prophets applied the words
in mockery to his utterances as being “burdens” in the ordinary sense
of the word, oppressive and intolerable.
The Pulpit commentary is similarly helpful. BDB also has "oracle" as the one of the idiomatic meanings of this Hebrew word as well -
III. מַשָּׂא noun masculineIsaiah 14:28 utterance, oracle (compare
נשׂא 1b (6); GfJeremiah 23:33); — ׳מ absolute Isaiah 14:28 +; usually
construct Isaiah 13:1 +; — of prophetic utterance: 2 Kings 9:25;
Isaiah 14:28; Ezekiel 12:10; 2Chronicles 24:27 (with עַל); בָבֶל ׳מ
Isaiah 13:1, מוֺאָב ׳מ Isaiah 15:1, compare Isaiah 17:1; Isaiah 19:1;
Isaiah 21:1,11; Isaiah 22:1; Isaiah 23:1; Isaiah 30:6; Nahum 1:1; בערב
׳מ Isaiah 21:13 is later insert (Di); ׳מ = revelation, אֲשֶׁר חָזָה
חֲבַקּוּק הַנָּבִיא ׳הַמּ Habakkuk 1:1; ׳י ׳מ utterance of ׳י Jeremiah
23:33,34,36,38 (3 t. in verse) (compare 2 Kings 9:25), see also 2
Kings 9:33 b (read אַתֶּם הַמַּשָּׂא), with word-play, — followed by
וְנָטַשְׁתִּי 2 Kings 9:36 b; ׳דְבַר י ׳מ Zechariah 9:1 (+ בארץ),
Zechariah 12:1 (+ עַליִֿשְׂרָאֵל), Malachi 1:1 (+ ׳אֶליִֿשׂ). —
Proverbs 31:1 see I. מַשָּׂא, p. 601 above; in Proverbs 30:1 read
מִמַּשָּׂא from Massa (Mühlau, De), or הַמַּשָּׂאִי (Wild), which
however is perhaps not original, but borrowed from Proverbs 31:1
(compare Wildon the passage FrankenbSpr. p. 5; corrupt name of Agur's
home or tribe, Kau).
Now, Jeremiah's inspired text is (typically) very clever in that he employs this word מַשָּׂא (massa) in a dual sense - of both the oracle/message, and, of the people who have become a burden to God.
The pulpit commentary summarizes the meaning well -
Verse 33. - What burden? etc. The Hebrew text, as usually read, is
extremely difficult; the Authorized Version is entirely unjustifiable.
It is just possible to explain, with Ewald, "As to this question, What
is the burden? the true meaning of the word is that," etc. But how
harsh and artificial! By a change in the grouping of the consonants
(which alone constitute the text), we may read, Ye are the burden. So
the Septuagint, Vulgate, Hitzig, Graf, Payne Smith. We must in this
case continue, and I will cast you off, as the same verb is to be
rendered in Jeremiah 7:29; Jeremiah 12:7. Instead of carrying you with
the long-suffering of a father (Deuteronomy 1:31; Isaiah 46:3, 4;
Isaiah 63:9; Psalm 28:9), I will east you off as a troublesome load
(Isaiah 1:14).
