On the flop I seem him chk/c mostly with draws and Jx type of hands. I don't think he has any 4x hands in his range, he would probably resteal preflop with A4 and the rest is not part of his range. I also feel he would probably chk/r most of his fdraws here. So that leaves me with Jx hands and maybe QT for and OESD. When he bets out on the river I strongly feel I have the best hand, but maybe my thinking is flawed here?
His stats:
47/29/13% 3b over 18 hands filtered for HU.
Ongame Network NL Hold'em Turbo No Limit Hold'em Tournament - t100/t200 Blinds + t20 - 2 players - View hand 1602145
DeucesCracked Poker Videos Hand History Converter
Hero (BTN/SB): t4720 M = 13.88
BB: t2780 M = 8.18
Pre Flop: (t340) Hero is BTN/SB with Q 
A
Hero raises to t400, BB calls t200
Flop: (t840) 4 
K J 
(2 players)
BB checks, Hero bets t400, BB calls t400
Turn: (t1640) 4 (2 players)
BB checks, Hero checks
River: (t1640) Q (2 players)
BB bets t800, Hero calls t800