9 For what thanks can we render to God for you, for all the joy with which we rejoice for your sake before our God,
10 night and day praying exceedingly that we may see your face and perfect what is lacking in your faith?
for what thanks (v.9) — the idea being that no amount of thanks would be sufficient for the great amount of joy they have received
render (v.9) = give in return for, pay back in equivalence
for your sakes (v,9) — on their account, because of them — I think Paul was saying that he rejoiced because of them, but also that he was rejoicing for them, for how they were responding and what that meant for their faith
night and day (v.10) — similar to “without ceasing” in 1 Thessalonians 1:3 and 5:17 — I think this is indication that prayer can be far less formal than what we generally think of. Paul states repeatedly that he prays constantly and yet he also sleeps and travels and teaches and makes tents and writes letters. I believe that he did all these things with a conscious awareness of God and a constant desire to be doing His will and that that is considered to be prayer. In this case, I think Paul’s love and concerns for the Thessalonian believers was constantly on the forefront of his mind and as often as he thought of them, he thought of God’s will for them and for himself concerning them.
praying (v.10) = deomai, used in the New Testament for “requests addressed to God” with an element of worship
exceedingly (v.10) = superabundantly
perfect (v.10) — katartízo (definition in Vine’s quote below) — This is a different word than teteleiomai, which means “to bring to an end,” “to complete,” as in Philippians 3:12: Not that I have already attained, or am already perfected; but I press on, that I may lay hold of that for which Christ Jesus has also laid hold of me. And it’s different from peploromenoi, which means “accomplish,” “finish,” “fully complete, ” “perfect” as in Colossians 2:10: And you are complete in Him, who is the head of all principality and power.
perfect (v.10) — This word is used of mending nets, Matthew 4:21; Mark 1:19, and is translated “restore” in Galatians 6:1. It does not necessarily imply, however, that that to which it is applied has been damaged, though it may do so, as in these passages; it signifies, rather, right ordering and arrangement. — Vine, page 50
what is lacking (v.10) — There was more that Paul wanted to teach them that he hadn’t had a chance to say because he was chased out of Thessalonica.
faith (v.10) — here, probably referring to the body of doctrine (as he goes on to teach in the remainder of this letter), rather than their confidence or trust in God.