Weird spot with aces ($5)

[Yabasa]

Full Tilt No-Limit Hold'em, 5.5 Tournament, 15/30 Blinds (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

SB (t1500)
BB (t1500)
UTG (t1500)
UTG+1 (t1500)
Hero (MP1) (t1500)
MP2 (t1500)
MP3 (t1500)
CO (t1500)
Button (t1500)

Hero's M: 33.33

Preflop: Hero is MP1 with A, A
2 folds, Hero bets t105, 4 folds, SB calls t90, 1 fold

Flop: (t240) 7, K, K (2 players)
SB checks, Hero checks

Turn: (t240) 5 (2 players)
SB checks, Hero bets t200, SB raises to t400, Hero calls t200

River: (t1040) K (2 players)
SB bets t995 (All-In), Hero calls t995 (All-In)

Total pot: t3030

First hand of the tourny so no reads but i played 63 hands with him before, 25/3.

Flop: How many worse hands do you get value from on that board?

Turn: What range do you give him after his min raise? Is it possible for him not to have a king or full house?

River: Not much to say here.

[Fielmann]

Flop: What are his post-flop stats? (Aggression factor, fold to c-bet and the like.)
Against a typical $5.5 donk I'd always bet, because as it's unlikely that this flop hit us, he might decide to continue with any pp or even without a pair. Against a tight opponent I don't mind an occasional check, hoping he'll pick something up by turn.

Turn: Yea, it's trips/set extremely often, but I couldn't fold. Shoving wouldn't help either.

River card is very lucky for you. What do we do if it's a blank and he still shoves?

[Yabasa]

Don't know how meaningful post-flop stats are with such a small sample size but here are some of them:

Folded to flop bet: 71 (5 out of 7)
Aggression factor: 1.6
Flop raise: 0

River card is very lucky for you. What do we do if it's a blank and he still shoves?

That's exactly what i was asking myself on the turn. It's hard to see how we can be best though. He could be value owning himself with TT-QQ but i don't think he's doing that or bluffing with AsQs often enough to warrant a call.