did you have stats on villain?
When the villain is tight, his reraise represents AAAKKKQQJJ. When he is looser you can add AQ. When he is loose agressive you can even add more, although you have to keep in mind, that thinking loose players are aware that you raise utg.
To simplify we put his range on AAAKAQKKQQJJ. In this case check raising if no overcards come on the flop is dangerous, but at least you know where you stand.
As 4 of his 6 possible hands are overpairs it becomes a matter of set minings as well (an interesting topic on this part is http://www.liquidpoker.net/poker-forum/478298/setmining_from_blinds.html)

A simplified EV calculation: Your change to hiy your set is around 11%. We dont assume an overset. We assume you check raise when no ace, king or queens pop up (33%), which costs you an extra $7)
Villain will never lay down aces: 1/6 (of his range)* (1/9* 35.25 - 8/9 (2/3*2.05 + 1/3 * $9.05)) = 0.03
Villain will only lay down kings when an ace comes (~25%), inwhich you win at most one extra bet: 1/6 * 3/4* (1/9* 35.25 -8/9 (2/3*2.05 + 1/3 * $9.05)) + 1/6 * 1/4 * (1/9 *7.10 - 8/9 (2/3*2.05 + 1/3 * $9.05)) = 0.03 - 0.12 = -0.09
Villain will only lay queens when an ace or king comes (~50%): 1/6*1/2 *(1/9* 35.25 -8/9 (2/3*2.05 + 1/3 * $9.05)) ) + 1/6 * 1/2 * (1/9 *7.10 - 8/9 (2/3*2.05 + 1/3 * $9.05)) )= 0.02 - 0.25 = -0.23
Villain will only lay down jacks when an ace, king or queens comes (~66%) :1/6*1/3 *(1/9* 35.25 - 8/9*(2/3*2.05 + 1/3 * $9.05)) + 1/6 * 2/3 * (1/9 *7.10 - 8/9*(2/3*2.05 + 1/3 * $9.05)) )= 0.01- 0.34 = -.033
Villain will only play AK further than flop if he he hits the ace or king (~50%): 1/6*1/2 *(1/9* 35.25 - 8/9*2.05) + 1/6 * 1/2 * (1*7.10)= 0.17 + .059 = .0.76
Villain will only play AQ further if an ace comes or a toppair queens (~40%):1/6*4/10 *(1/9* 35.25 - 8/9*2.05) + 1/6 * 4/10 * (1*7.10)= 0.13 + 0.47 = 0.6
In the two last equations I assume you win one bet of $3 if no ace, king or queens are on the flop.

Total EV: 0.03 - 0.09 - 0.23 - 0.33 + 0.76 + 0.6 = 0.74
Hence a marginal play
Keep in mind that by check raising you loose value against overpairs and win against AK/AQ.
If villain is tight you can delete AQ.
That's why I would plat it against a tight villain for set value. However against a loose player his range might even be bigger inwhich you EV would rise with check raising.

PS the equations are complex, so it could be very possible I made a mistake