[Raxxmataxx]

It seems you have something like 50%-53% on the river, prior to any actions. But for you to have that good equity on the bet means that he'll never raise you off with a worse hand and pay off with a ton of really bad hands.

So I don't think you actually have a pure valuebet here, but it may still be better than checking if he is passive and mostly aren't going to bluff when you check while still valuebetting lower hands. Ie, you lose a little less on the bet by betfolding than by checkcalling. If he is passive allround and won't value bet hands like 8:s there's much less clear value in the bet.

I don't think a bet is clearly bad. Especially as his really good 4-card hands on 6th are very unlikely.

I am pretty sure that this is checkcall if we assume perfect play on the river only for both of you. Especially since your paired ace makes this hand not all that good among your possible hands. Assuming you're not crazy on 3d and bet every hand on 5th, T7 is in your bottom 15%, on the river.