This passage continues Paul's meditation on weakness and strength, after being accused of being weak in person but strong in his letters, he argues that his weakness is the humility of Christ by which God's power works in the Corinthians.
2 Corinthians 12:9 (KJV 1900)
9 And he said unto me, My grace is sufficient for thee: for my
strength is made perfect in weakness. Most gladly therefore will I
rather glory in my infirmities, that the power of Christ may rest upon
However he cautions them that if they want to see power rather than weakness, they will see power, but it will be God's power working through Paul's weakness.
2 Corinthians 13:2–4 (KJV 1900)
2 I told you before, and foretell you, as if I were present, the
second time; and being absent now I write to them which heretofore
have sinned, and to all other, that, if I come again, I will not
spare: 3 Since ye seek a proof of Christ speaking in me, which to
you-ward is not weak, but is mighty in you. 4 For though he was
crucified through weakness, yet he liveth by the power of God. For we
also are weak in him, but we shall live with him by the power of God
Weakness here refers to not using your strength, rather than a lack of strength. It was because Christ did not use his strength, but submitted to abuse on the Cross, that the Father's power worked through Christ.
This is what Paul means when he says Christ was "crucified in weakness" (e.g. he did not use his own strength to prevent being killed), and so we also do not use our strength when we are "in Christ" but rely on God's power. Thus we [referring to Paul and his ministers] are weak in Christ which allows us to be vessels through which God's power works.
When we try to be strong -- use our own power -- then we step out of Christ and are working with the power of the flesh, our own strength, and then the power of God is not at work. To have the power of God at work, we need to not use our strength, but rely on God's strength.
Ralph Martin has a good commentary on this in WBC:
Paul’s christological understanding fits well into his argument of
13:4. Christ is both weak and strong. Barrett is right to point out
that Christ’s weakness, as exhibited in the crucifixion, is not the
result of a lack of power.1298 When Christ chose the cross, he did so
because he was acting in God’s power. Yet he assumed ἀσθένεια,
“weakness,” as a role. In taking God’s will to be his own, Christ
acted in power, despite the fact that the world would think otherwise
(cf. Mark 15:30–32). His death on a cross was his own choice and not
to be understood as submission to alien powers, such as
satanic-demonic forces, as in gnostic ideology.1299 Always the weak
Jesus remains the subject in dependence on God,1300 and the stress on
his “weakness” is not simply a sign of true humanity (although it is
that). Rather, Paul is polemicizing here against a theologia gloriae,
“theology of glory,” that viewed Christ as a powerful figure in his
Ralph P. Martin, 2 Corinthians, ed. Ralph P. Martin, Lynn Allan Losie, and Peter H. Davids, Second Edition., vol. 40, Word Biblical Commentary (Grand Rapids, MI: Zondervan, 2014), 672–673.