3bet size too small here out of position. Size up if 3betting from the sb. Betting to represent an over pair on this board is not an ideal thought process to have. As opposed to thinking in terms of one hand in isolation, you need to consider how your range does on this board overall. While you do have most of the over pairs here that villain does not, villain also has pairs. This board also interacts well with the ranges that you said you expect villain to have.

Being out of position you should be 3 betting 3.5x or even 4x.
I dont mind the cbet the flop but its not ideal as the middling cards is what he will have some times. You can bet the river though as thats more likely that you will have that and he wont.

When you say you're trying to rep overpairs it's true you have JJ+ but you also have a lot of AK,AQ,AJ,KQ combos. A T high flop (especially with a 9) tends to favor the BU 3-bet calling range, for that reason I think a x/c is also fine.

Size up preflop to atleast 0,27. Betting flop is perfectly fine in general, turn check is probably good aswell. You could bluff river.