I'm not sure about evolution over time. my observations seem to point towards there being a greater diversity of axe weights during the same period that there was a greater diversity of axe patterns. So during the golden age of axe manufacture and use, there was probably the greatest variety of patterns and weights to meet the needs of all users and use types. In terms of why you don't see the super heavy axes any more - is same reason why you don't see the other diversity of axe patterns any more. very few people's livlihood depends on axes. there is less need for all types of axes which includes the heaviest axes, and even fewer people these days who would be able to skillfully utilize a heavy axe.
For american axe patterns my observations are as follows.
heaviest axes seem to be dayton patterns. I've seen daytons up to 7lbs. I own an old 6lb dayton, true temper
next heaviest seems to be kentucky patterns - I've seen several over 5lbs
Rafting patters seemed to be usually 4-5 lbs, so on the heavy end but not the heaviest.
I've seen 5lb jerseys and own several 4 - 4.5 lb jerseys
I own vintage double bit axes that are 4.5 and 5lbs, western and michigan patterns. I used to have a huge peeling double bit. don't remember what it weighted. I don't think more than 5lbs though.
Jerseys seem to be one of the smaller patterns - they seem to be most commonly 3lbs, but have seen them up to 4lbs. I'm sure there were heavier examples, but not commonly.
Now, the heaviest "old" axes seem to be the english axes. I've seen tons of older english made axe heads that weigh 6-7lbs. I'm not sure what the english were doing with those heavy axes, maybe felling timbers for shipmaking or something. I imagine those long bitted short polled heavy axes really sucked to swing accurately. no thanks.
In the present day, I think most 'heavy' axes are used as fallers axes by chainsaw sawyers. These tend to be 4-5lb axes with short handles. there is also a category of people who use 4-5lb axes for splitting wood, though most woodsplitters use mauls which are much better suited to the task for most hardwoods. The heaviest axes used today are firemans axes, but those are specialty axes which you excluded from your inquiry.
in terms of size/weight ratios - I have only a small sample size, but I do have true temper daytons that range from 3 3/4 - 6lbs and the axe heads increase in all dimensions as weight increases. so total length, bit length, and eye thickness increases.
however, I've noticed that with jersey axes, total length and bit length doesn't seem to increase a lot with a weight increase from 3 - 4.5 lbs so most of the weight increase must be in eye and poll thickness, as most true temper jerseys measure approx 5.5" x 7" regardless of weight. This is obviously a generalization and there will be slight measurement variations with weight, but not as much as would be predicted by the weight change.