PokerStars No-Limit Hold'em, $0.25 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Hero (UTG) ($49.50)
MP ($26.70)
CO ($38.35)
Button ($5.45)
SB ($25.80)
BB ($25.65)

Preflop: Hero is UTG with K, A
Hero raises to $1, 2 folds, Button calls $1, SB calls $0.90, 1 fold

Flop: ($3.25) A, 10, 6 (3 players)
SB checks, Hero checks, Button bets $2, SB calls $2, Hero raises to $6, Button calls $2.45 (All-In), SB raises to $12, Hero raises to $47.25, SB calls $12.80 (All-In)

Turn: ($57.30) 8 (3 players, 2 all-in)

River: ($57.30) Q (3 players, 2 all-in)

Total pot: $57.30 | Rake: $2.85

SB is 24/13/0.89, Button is 45/2/3.

I feel like the button could have anything here, from a weaker ace to a straight/flush draw. SB, having been so passive so far, I feel had me beat, with a set of Ts or 6s. Am I still right to make this call given this?

Standard except I bet the flop

Lotsa different ways to play this, but yeah, bet the flop. If you bet the flop 3/4 of the pot, SB's actions will be in better context I think.

Only reason for my check was to induce the LAG btn to bet so I could come over the top of him with confidence if the SB just called or folded. Not how it went though.

There's nothing to be gained by checking here.
The shortie is calling with virtually any pair.
I think you need to charge the SB some admission/get some value from the hand at the start.
And again, for emphasis, we didn't flop a set or quads, we flopped one pair.
We're likely ahead, but we need to be shipping/defending, and not checking with one pair hands.