PokerStars - $3.16+$0.34|200/400 Ante 25 NL - Holdem - 3 players
Hand converted by PokerTracker 4
Hero (BTN): 5,848
SB: 1,947 (VPIP: 29.55, PFR: 11.11, 3Bet Preflop: 4.55, Hands: 90)
BB: 5,705 (VPIP: 18.58, PFR: 19.27, 3Bet Preflop: 3.57, Hands: 117)
3 players post ante of 25, SB posts SB 200,
BB posts BB 400
Pre Flop: (pot: 675) Hero has K

K
Hero calls 400,
fold,
BB raises to 800,
Hero raises to 2,000,
BB calls 1,200
Flop: (4,275, 2 players) Q

T

A
BB checks,
Hero ?
The limp was to induce action. Moreover, the villain had folded to every steal up to this point. He hasn't done anything fancy so far, so his preflop call of the 3bet threw me off, as it was 25% of his stack.
What kind of range would you put him on? Is this flop a shove, given the pot size?