I have a semi-read on SB. 24/12/11 over about 50 hands. Most of his PFR's are min-raises. He will usually give up when he misses the flop so I've got to assume he's strong here.

8 handed
BB [Th]
SB - $51.65 after posting and I cover.

UTG+1 limps, Button limps, SB min-raises to $1, all 3 of us call.

[9h][6h] Pot $4
SB bets $4, I call $4, UTG+1 raises to $12 (only has $6.05 left), Button folds, SB calls $8 more, I call $8 more because there's $32 in the pot (4-1 odds)

Pot $40.00
SB bets $6.05, I call, UTG+1 calls all-in for $6.05

Pot $58.15
SB has $32.85 left and checks. I have $48.80 and as I said, UTG+1 is already all-in and there is no sidepot.

Bet half his stack?
Try to look sneaky and push since I think SB has a fairly big hand?

Just shove it in there, the pot is really big and he has only alot less than a PSB left.

If you have a read that he'll call smallish river bets then you can bet 20$, but most of the time if he'll call 20 he'll call the 38.