This hand escalated quickly. the table was playing pretty fast. I am interested to hear what the community thinks about what to do on the turn in this spot.

UTG (HERO): $230
MP: $350
BB: $250

Preflop Pot ($3): Hero has KsQh
Hero raise to $10 (standard raise at this table)
MP Calls $10
BB Calls $10

Flop Pot ($33): Kd Qc 8h
BB Check
Hero bet $20
MP call $20
BB raise to $40
Hero call $40
MP call $40

I bet this flop because i have a pretty solid range advantage and want bet to get some value. When x/raised I think that 88 is a possibility from the BB. and the MP's c/c reaks of some sort of straight draw or KJ / K10

Turn Pot ($153): 10s
BB bets $50
Hero ?

This is dangerous turn because MP has all AJ in his range. The BB betting out here feels strong as well.

What would you do in this position and what is your reasoning? I know what i did and I do not believe it was the right play. Any thoughts appreciated!