I would probably make it something like 6k to go as it looks like a squeeze and if the original raiser has hands like KQ+ or AT+ etc then he may well elect to jam it feeling he has f/eq. All jamming does here is folds out hands you want to have shove on you and you only get called by either better hands or tied hands usually although someone could call with AJ+ maybe and some medium / high PPs. A shove is probably not terrible but I feel in the long run inducing an opponents shove will be more profitable.

Its not so much inducing a 4bet from AQ specifically but more about just giving your opponent the chance to take a punt at a sizeable pot with a weaker dominated hand. Basically, we want to give the oppponent opportunity to make a mistake. Most players will either jam/fold when faced with this squeeze, certainly at mid/high stakes I expect.

Shoving is obviously never going to be bad here but when you shove you do get the “I've a pair flipping with AK” brigade calling you with their 55, 66, etc and you don't really want that in this spot either.

Personally I think the times you get people to make a play at the pot is worth running the risk of getting called in 2 spots. Also, quite often you will be heads up and win the pot with a c-bet or you hit the flop anyway.

With 20bbs I'm shoving it all day, 25bbs+ I start thinking more about 3 betting and trying to get value that way. It's probably close either way as to what is optimal though.