Any way to play JJ better here?

***** Hand History for Game 2893457295 *****
$25 NL Texas Hold'em - Monday, October 17, 23:51:52 EDT 2005
Table Table 68491 (Real Money)
Seat 4 is the button
Total number of players : 10
Seat 1: sw33tns0ul2 ( $20.95 )
Seat 2: zeke714 ( $56.19 )
Seat 3: jandje ( $28 )
Seat 4: getere ( $33.25 )
Seat 5: Paul01111 ( $24.70 )
Seat 6: Ramstone ( $7.30 )
Seat 7: mathewsw ( $47.34 )
Seat 10: rappel ( $9.03 )
Seat 8: jal3333 ( $23.95 )
Seat 9: coffeecan26 ( $14.65 )
Paul01111 posts small blind [$0.10].
Ramstone posts big blind [$0.25].
** Dealing down cards **
Dealt to jandje [ Jh Jd ]
mathewsw folds.
jal3333 folds.
coffeecan26 raises [$1].
rappel folds.
sw33tns0ul2 folds.
zeke714 folds.
jandje calls [$1].
getere folds.
Paul01111 folds.
Ramstone folds.
** Dealing Flop ** [ 2d, 6s, 6c ]
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coffeecan26 checks.
jandje bets [$2].
coffeecan26 calls [$2].
** Dealing Turn ** [ As ]
coffeecan26 checks.
jandje bets [$3].
coffeecan26 calls [$3].
** Dealing River ** [ Td ]
coffeecan26 checks.
jandje checks.
coffeecan26 shows [ Qs, Ah ] two pairs, aces and sixes.
jandje doesn't show [ Jh, Jd ] two pairs, jacks and sixes.
>You have options at Table 65026 Table!.
coffeecan26 wins $11.75 from the main pot with

check behind on the turn. this is 25nl, he has an ace, and never bets.

but seriously. no, betting out is correct, checking behind the river is correct.

Ni Han

The turn bet was to get a non ace to fold or a weak ace to fold. Once he called, I knew he had it. I was ready to fold the river.