The Nuts and a tough 2/4 river decision

[Marlow]

SB (400) is a complete unknown. BB (~140) is a slowly dying loose passive who has done nothing noteworthy. Hero covers both opponents. It's a 4-handed game.

UTG folds, Hero raises to 12 with AcKc, SB and BB call.

Pot: 36

Flop: Qc 9d 8c

SB leads with $20, BB calls, Hero calls.

Pot: 96

Turn: Ad (Qc 9d 8c)

Checks around. (BTW, I'm very suspicious of SB at this point, which is why I check.)

Pot: 96

River: 5c (Ad Qc 9d 8c)

SB checks, BB makes a horrible (for me) underbet of $12. Hero...?

As I see it, SB's made hand just got snapped off, and he prolly knows it. SB could have caught a little something at the end, or is just stealing or clueless. But he could also have a weaker flush and is trying to induce a big bet (that's he's too skeered to make). What's the best raise amount here and why?

Marlow