[Hand Analysis] 5NL, facing turn shove in 3bet pot.

Hi guys, I'm sure this is a standard spot in the long run, but I'm just unsure about whether or not I made the correct play in this spot.

I had very little hands on villain, but is looking to turn out laggy at 35/35 over ~30ish hands.

UTG: $8.86
CO: $5.67
BTN: $5.00
Hero (SB): $11.99
BB: $1.81

Pre Flop: ($0.07) Hero is SB with K A
1 fold, CO raises to $0.15, 1 fold, Hero raises to $0.45, 1 fold, CO calls $0.30

Flop: ($0.95) A 4 7 (2 players)
Hero bets $0.50, CO raises to $1.45, Hero calls $0.95

Turn: ($3.85) K (2 players)
Hero checks, CO bets $3.77 all in, Hero??

I think preflop raising is fine, as I'd rather have the initiative and get value from worse. On the flop is where I'm not so sure about. I feel like he represents so little value hands, only A7, A4, 44 and 77, with A4 and A7 folding pre most likely. Because of this I thought that a lot of his hands in this position could be semi-bluff heart draws, or potentially just 56, that I felt the best play was to just flat and call off any non heart turn.

However, when the heart comes on the turn that gives me two pair I'm not sure if it is a fold or call. We move ahead of the A4s and A7s that were ahead on the flop, but all of the heart semi-bluffs got there. I'm also not sure if he does this with his sets when the flush gets there. There's also the possibility of him raising a worse ace, but I'm not sure whether he would shove turn, although having the J or Q of hearts might allow him to make this play, which we are ahead of.

In general against unknown an unknown, are you stacking off in this spot?