JJ in reraised pot 3w vs loosies 200NL

[pleyya]

UTG was about 70/50/5 over a couple of 100 hands through mining, this was my first hand with him, he was min raising almost all his raises. BB was 70/10/1 and seemed quite passive. He called raises alot so i give him no credit.

200 NL All fullstacks
UTG opens to 4
3 folds
Hero on button reraise to 16 with JJ (no spades)
BB coldcalls
UTG calls
*** FLOP *** [S8 S6 S9] potsize 49
UTG checks
BB bets 34
Hero...?????

I feel like if i raise i have to stack off vs BB since flop is so drawy, flop is to drawy to call, and folding seems weak. I was lost here.