He 3-bet you preflop, and checking to the preflop aggressor on a A high board is completely standard. Why do you think, checking the flop cost you money? Because you know, what he had, and that making him fold would have saved you money? This is the kind of results oriented thinking, that is preventing you from developing a good strategy.
Where you lost value was by not betting the river. You were still way ahead of his range, and you could certainly get called by all his worse two pair or even just top pair like AQ. So no. We never fold top two on this river, we bet it for value. His range for 3-betting is not only JJ+, unless you have a big HUD-sample showing a 3% or lower 3-bet, and even then you also have to include at least AK.
Without that info he can have any suited ace, and he can also have all AQ and possibly even AJ, which would be awesome, since then he rivered a worse two pair. Everyone are not nits, especially not in a 5-handed game. Admittedly there might be a bit less 3-betting going on at 2NL, but without HUD-data you still cant narrow someones range down to only big pocket pairs.
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