NL2 KQ two pair getting shoved OTT

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NL2 KQ two pair getting shoved OTT

PokerStars - $0.02 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

BTN: $1.10 (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 1)
SB: $2.42 (VPIP: 100.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 1)
Hero (BB): $2.61
UTG: $1.91
MP: $2.42
CO: $3.95 (VPIP: 13.48, PFR: 10.11, 3Bet Preflop: 0.00, Hands: 90)

SB posts SB $0.01, Hero posts BB $0.02

Pre Flop: (pot: $0.03) Hero has Kh Qs
UTG calls $0.02, MP calls $0.02, fold, fold, fold, Hero raises to $0.10, UTG calls $0.08, MP calls $0.08

Flop : ($0.31, 3 players) As Qh 4s
Hero bets $0.15, fold, MP calls $0.15

Turn : ($0.61, 2 players) Kc
Hero bets $0.44, MP raises to $1.91, fold

MP wins $1.44

I'm not sure what is his limp/call range? Looking at his stack, we could say he's a fish, so I guess his range has all kinds of hands, even AQ, AK, QQ+ etc. I'm not sure if we can call this, because I don't think even a fish would shove OTT here with some weak A. Any thoughts? There're too many hands that beat us, because it's really hard to put him on a range. But let's try to break it down.

Hands that beat us: QQ+, AK, AQ, 44, JT.
Hands that don't beat us: A2, A3, A5-AJ, flush draws, weaker pocket pairs and random air.

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