Just wondering what you would do with my stack in this situation.

Full Tilt Poker Super Stack $15K Guarantee No Limit Hold'em Tournament - t140/t280 Blinds + t25 - 8 players
The Official DeucesCracked.com Hand History Converter

CO: t12914 M = 20.83
BTN: t19523 M = 31.49
SB: t19605 M = 31.62
BB: t7705 M = 12.43
Hero (UTG): t20110 M = 32.44
UTG+1: t9398 M = 15.16
MP1: t11778 M = 19.00
MP2: t31229 M = 50.37

Pre Flop: (t620) Hero is UTG with 8 8
Hero raises to t875, 4 folds, BTN calls t875, 2 folds

Flop: (t2370) 3 3 5 (2 players)
Hero bets t1675, BTN raises to t3350, Hero ?

Call and reeval.

Also, raise smaller pre. 700 is fine.

Pretty much yeah...

I find that min re-raises are semi-bluffs, at best, to chase out holding like AK/AQ or other suited Broadways, for example, that missed a flop like this. At the same time, you have to be wary of 99-JJ, as these are often holdings that will only call a PF raise in order to try and see a safe flop. With depp stacks it's probably better to RRPF with a holding like that, but a lot of people don't want to start spewing and might be worried about getting 3-bet.

At the same time, 44-66-77 is easily in the mix, too...

I think a check raise or check call would be better on the flop.(even if he checks behind you are giving a free card on a small pot)
By leading and getting raised it's really hard to play the hand afterwards. (you are probably checking the turn and giving a free card on a bigger pot)

calling the flop and folding the turn just seems bad imo.

Who said we were folding the turn?

I would def consider throwing some chips in the middle if an A comes on the turn, assuming we only call (and not re-raise) the flop. If villain has a slightly better PP, there are a bunch of scare cards that can come on the turn that would warrant some kind of move.