T7s falls into a region of my range I don't really like to 3bet BvB. BvB you should mostly 3bet hands that are clear calls vs 4bet and clear folds, but you can have some in between hands like this one. I rather just use a hand like A5o, K6o, 97o etc as my weak 3bets if villain folds too much.

Turn is a very high frequency barrel spot because the board texture connects weakly with SB call vs BB 3bet. Your exact hand plays well as both bet and check (a mix spot), and it's fine to check some FDs and bluff weaker hands here.

I think you have a clearly +EV bluff on the river and have no EV as check back (BXB bluffing are usually +EV in most spots vs population but not always higher EV than check back).

I was thinking I would bet the turn and than check that blank river. But Kalupso's point about opponents range not connecting well with board has me second guessing myself.

have to bluff, it is not midstakes