€10 NL HE MTT: fall victim to villain slow playing his set

It's the final table of a satellite and the prize pool was 3 x €50 tickets. There were only 5 players left and there was little action.

Starting stack:
SB: 3.97 BB
BB: 13.08 BB
UTG: 19.68 BB
Hero: 11.67 BB
BTN: 10.12 BB

Everyone paid ante 0.13 BB
Pot became 0.63 BB

SB paid 0.5 BB
BB paid 1 BB
Hero got dealt As7c
UTG folded
Hero called 1 BB
BTN folded
SB called 0.5 BB
BB checked
Pot became 3.63 BB

Flop was Ac6d6s
SB checked
BB checked
Hero bet 2.86 BB
SB called 2.84 BB and became all-in
BB called 2.86 BB
Pot became 12.15 BB + 0.03 BB

Turn was 5d
BB checked
Hero checked

River was 2h
BB bet 9.1 BB and became all-in
Hero called 7.69 BB and became all-in
Uncalled bet 1.41 BB returned to BB
Pot became 12.15 BB + 15.41 BB

BB showed Jh6h, forming 6s[6h]6dAc[Jh], a triplet of sixes
Hero showed As7c, forming [As]Ac6s6d[7c], two pairs aces up
SB showed Ad2d, forming [Ad]Ac6s6d5d, two pairs aces up

BB won 27.55 BB and killed SB (5th) and Hero (4th). The bubble bursted and the tournament ended.

Hero fell victim to BB slow playing his triplet. Which step went wrong here?

Had to re-read because I read it wrong initially. With SB so short, I think you can probably fold pre here and avoid this. There will be better spots to play.

Preflop
Especially near the bubble of a satellite limping here is really bad. You want to use a push or fold strategy, and this would be near the bottom of my pushing range. You dont want to see a 3-way flop with A7 offsuit, and you also dont want to allow BTN or BB to jam on you, because then you will need to fold.

Flop
As played this is way ahead, way behind spot, so I dont see much value in betting. Just try to get to showdown as cheaply as possible and hope, top pair no kicker is good.

Turn
Definitely check now as played.

River
As played this is a fold. You dont beat anything, that is betting for value, and there are no bluffs in BBs range. He overcalled on the flop on a board with no draws, so he has to have a made hand, and he still need to beat SB at showdown. So even if he somehow called with KJ or something, he would just give up now.

Results
If you jam preflop, then J6s almost certainly fold, and you dont get yourself into this postflop mess. Jamming is profitable, and it also protect you from making unnessesary postflop mistakes. Maybe you even get called by SB, which you would actually have beat, since your kicker still played on the river.