I think you just need to 4bet this preflop. You're just pushing a lot of equity, and these aces should be able to realize a lot of equity, especially while being ip. I'd only really flat very unconnected aces here. As played, I think you need to call vs the jam as you're probably at the top of your range. Card removal is obviously important too, but other than sets with a 6 for a side card, you're not going to have many good blockers here. Also, regarding the title of your thread: just because you lost doesn't mean you played aa terrible ;).

My reason for not 4betting preflop would be if I had a good read on villains postflop tendencies and therefore prefer to play IP with a higher SPR.
As played: Do you check back the turn to throw him off the trail or because you are worried of the nutz? I would just bet here myself, he can still have worse hands to call and hands with EQ that fold.
As played Im not sure about the river. I am at PLO10 where a river raise is the nutz so often that you dont even have to think about it, but here I can see leveling myself into call, thinking that since we checked back the turn, villain won't put us on the straight but rather a set and try to get us off by jamming.

I think you overlooked a "not" in my post?

I would always 4b pre. You're guaranteed to push equity and give him the chance to 5b. 1,4 SPR is not bad with these aces.

But if I took this line I would strongly consider raising the flop planning on getting it in. Especially if you think he's viewing you as capable of attacking boards where you have an advantage, at least in terms of 2 pair plus hands. You probably have 3 times as many of those as him here. He can easily not believe you and jam overpairs, straightdraw and pair+gutshot type of hands. As played I'm calling as well even though it might be a leak in these games.

Can someone give me some advice where I could learn more about SPR?

4bettin creates SPR around 1,5 for the flop. That is the borderline IF opponent has premium ace-cracking hand he plays perfectly on the flop. If his range contains any Axxx or pairs, your EV is positive.

So even with premium cracker, your opponent can't exploit you. With SPR 1,5 it's just EV0 flip for you. By just calling you create a problematic postflop which can easily lead to -EV line. 140bb deep I would 4bet this.