[SH nl50] KQs passive drawing

Poker Stars, $0.25/$0.50 No Limit Hold'em Cash, 5 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

CO: $56.50 (113 bb)
Hero (BTN): $50.50 (101 bb)
SB: $56.07 (112.1 bb)
BB: $50 (100 bb)
MP: $20 (40 bb)

Preflop: Hero is BTN with K Q
MP raises to $1, CO folds, Hero calls $1, 2 folds

Flop: ($2.75) A 4 2 (2 players)
MP bets $1, Hero calls $1

Turn: ($4.75) J (2 players)
MP bets $1, Hero calls $1

River: ($6.75) K (2 players)
MP bets $1, Hero calls $1

vs:

KQs plays very well against his open raise range. On deeper stacks I would 3bet for value. 40bb deep I should do it too or just calling? There is no squeezers on blinds.
as played:
villain cbet frequency is small so when he double barrels it is almost always Ax or better. He gives me good price to draw, flop and turn easy calls for me.
On river I wasn't able fold to 2bb bet, calls and hope for something like Jx