Hi Guys

Please give me your thoughts in regard to this hand:

PokerStars Hand #145027361704: Tournament #1399692490, $10.00+$2.50+$1.00 USD Hold'em No Limit - Level IV (30/60) - 2015/12/08 18:16:37 CET [2015/12/08 12:16:37 ET]
Table '1399692490 8' 9-max Seat #5 is the button
Seat 1: ElKarson21 (3330 in chips)
Seat 2: Ikmpnp (3123 in chips)
Seat 3: cznsnowy91 (4040 in chips)
Seat 4: pellompogos (2925 in chips)
Seat 5: gwen pe (1321 in chips)
Seat 6: greg6200 (2002 in chips)
Seat 7: Thisnoob (6446 in chips)
Seat 8: ebadia (2535 in chips)
Seat 9: orin159 (3147 in chips)
greg6200: posts small blind 30
Thisnoob: posts big blind 60
* HOLE CARDS
Dealt to This_noob [7s Ts]
ebadia: folds
orin159: folds
ElKarson21: folds
Ikmpnp: folds
cznsnowy91: raises 90 to 150
pellompogos: folds
gwen pe: folds
greg6200: folds
This_noob: raises 210 to 360
cznsnowy91: calls 210
FLOP [7h 2c Jc]
This_noob: bets 345
cznsnowy91: calls 345
TURN [7h 2c Jc] [7d]
This_noob: bets 878
cznsnowy91: calls 878
RIVER [7h 2c Jc 7d] [Ac]
This_noob: checks
cznsnowy91: checks
SHOW DOWN *
Thisnoob: shows [7s Ts] (three of a kind, Sevens)
cznsnowy91: mucks hand
Thisnoob collected 3196 from pot

OK, so my reasoning for checking the river is that I don't think I get called by worse when considering a range that reaches the river. I think the very bottom of villain's calling range would have to be AJ (in a vacuum); but I think AJ+ shows more aggression on either flop / turn so I dont think I can include this hand in his range. I don't think he has any 7's either as even A7s doesn't call many 3 bets (at least not that I've seen). So in this hand I think I'm either up against a single paired J or a made flush. If I shove, the J folds but the flush calls. So my decision here is to check and decide.

At the time of this hand I was leaning towards check-calling with a higher frequency than I would check-fold due to the fact that I have a very good bluff catcher (in that my hand is so under-repped).But now I'm realizing that his range is so well defined in this spot that I don't think I can call a shove as any J is happy to take the showdown. Is my reasoning flawed? Am I leaving money at the table by not shoving river? Are people at low stakes actually capable of shoving this without a flush?

As a side note, how often do you think people will turn their J into a bluff on this river to avoid a split / to get opponent off KK/QQ when checked to? Is it even worth considering?

Btw, villain is 26/21/25 in 39 hands so sample is largely useless :)