Hi!
So here is this bassic question about the checkraising here: Is it the most profitable play in this situation?
I think yes, if opponent cbets a lot. This is a dry board, and he will cbet at least 60% of the time I assume. Check calling multiple barrels is just too weak for me and way too passive.
In this case I think A6 is a little bit to strong to be check raising, we get into quite a few weird spots when we do.
However, I think hands like 69/67/65 (assuming we have them in our calling range, depends on his opening % and aggression) are better candidates to check raise with. This gives us more options on later streets. We can decide to turn our hand into a bluff, we can pick up 2 pair or trips, and its pretty easy to get away from on the flop if we dont suspect villan will 3bet us light.
So are we assuming villain barrels a large amount and doesn't 3 bet light? From op's description it seemed like he was getting barreled a lot, which probably correlates to villain being capable of 3-beting light, but I might be generalizing too much without a specific read.