NL10 AKs vs tight 3/4bettor?

I would just go ahead and shove this. He can have some bluffs in these positions and even if he 4bets just QQ+,AKo,AKs you have around 40% equity.
I think his 4bet range against you depends on what kind of info he has on you. You are probably bluff 3betting a lot from these positions and therefore villains 4bet range can be wider.

In BBvsBU we can play for stacks preflop.

I'm starting and I do not understand the meaning BBvsBU

This is the positions names
UTG - Under the Gun - 1st
MP - Middle Position - 2nd
CO - Cut Off - 3rd
BU (BTN) - Button 4th
SB - Small Blind - 5th
BB - Big Blind - 6th

BBvsBU - Big Blind vs Button.

I dislike getting it in with 40% equity, I don't believe this villain has bluffs in his range once 4betting so I like my play here. But thanks for your opinions on my hands :).

Well, because you have already invested some money in the pot you need only 46% to break-even. Add some fold equity there and you will have a profitable call.
Of course there is rake which takes some of that profit. How profitable will your shove be depends on how much villain is 4bet bluffing. If you believe he is not bluffing much, I think folding and shoving would be quite equal options on the long run. But now you might be overfolding vs 4bets and it could make you exploitable.

I don't think its a huge problem against someone who is 3betting 3%. But feels bad man to have to give up AKs.