[scotty34]

I edited my post. I think that they may check behind quite often if they are a solid thinking player. This would imply that villain recognizes you as a TAG/solid player as well. They will realize that you are not check-calling with nothing. They should know that you have either an A with a J+ kicker, or a K. You would have folded TT-QQ on the flop or turn, as you are not really beating anything that Villain would 3-bet except TT and JJ.

Villain will check behind almost always if they have TT-QQ. Villain will obviously bet a AK or AA, in which case we are losing anyways. Villain will bet an AQs some of the time, and check it others. I think that covers the range of 3-betting hands for most TAGs. Solid players realize that value betting is designed for playing against Loose-Passive players that call down with any piece of the board, not other TAGs.