HU vs donky guy

$0.25/$0.50 No Limit Hold'em Cash, 2 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.
Hero (SB): $43.40 (86.8 bb)
BB: $56.95 (113.9 bb)
Preflop: Hero is SB with 9
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Hero raises to $1, BB calls $0.50
Flop: ($2) 9
4
A
(2 players)
BB checks, Hero bets $1.50, BB calls $1.50
Turn: ($5) 3
(2 players)
BB checks, Hero bets $3, BB calls $3
River: ($11) 5
(2 players)
BB bets $5.50, Hero folds
early in the match he made some calls depite 3-bets, new opponent so it' pritty eay valuebet on the flop and on the turn. lead river 1\2 pot
what is the sence of doing that? I put him on Ax and just fold here.