BB is all in with less than one big blind, so is a dead pot.

SB is TAG. 19/14/7.9 stats

I feel I'm in a slightly ahead/way behind situation so I just call down to avoid bloating the pot with a crushed hand.

Same logic as the flop, so I continue to just call down.

At this point I feel that the SB would have shoved, or led small with a King, so by checking he has capped his range. The only other value hands I am against are aces, so by shoving, with ICM pressure would I get him to fold his Ace Queens enough to make a bluff shove profitable, or should I just check down with the second nuts, as hands like AT I feel would likely fold, and I wouldn't be able to get any value out of shoving into them.