To my eye, that's a very strange looking axe. I really don't know what use it would be where I live. Actually it is pretty close in shape to the imported things they sell as block splitters, but its sure not anything like our axes here. Its a bit hard to see what sort of grind it had, and that's really what tells you what the axe was meant to do and to what.
What you say about tool weights and physical size is true to a degree.
The heaviest hammer I ever saw used was used by the old bloke who used to be Pak Pauzan's striker. This man's family followed the trade of turning big rocks into little ones:- they made blue metal by hand. He was maybe 50 odd when he started work for Pauzan, and he used an enormous hammer that weighed in excess of 20 kilos. His technique was what I'd call "pendulum" he swung the hammer between his legs like a pendulum and on the return swing he carried it up above his head and down onto the anvil, in effect he turned himself into a pivot point, he really didn't use much strength at all. Just as well, because he stood about 5 foot nothing tall and weighed maybe 55 kilos. When he finished the strike, he'd slide the hammer off of the anvil, let it swing between his legs and do the pendulum thing again. He probably struck half as fast as a normal striker would, but each strike was like a steam hammer. He had been a rock breaker from the age of 6 or 7.
When I was doing a lot of forge work I used a 10 pound and a 12 pound hammer for heavy work and a 4 pound for one hand work. The technique to use a heavy hammer easy is to position yourself so that your back hand comes down onto your hip at exactly the same time that you strike the work on the anvil, then to lift the hammer you turn your hip as you lift, which causes your whole body to lift the hammer, not just your arms. This technique cuts effort by more than half.
If you use an axe handle that is the standard deers foot pattern that they sell in hardware stores, hickory will most certainly slap your hands, so will anything else, but if you use a handle that is the same design as used on racing axes you don't get a slap from any timber. These handles are bigger all round, they have a big hand filling knob as the deers foot and they are not smoothed down, but left with the rasp marks on. Use of one of these handles cuts the effort of axe work by a lot, for one thing, the axe will always go just precisely where you want it to, something that is often difficult to do with an ordinary hardware store handle.
Elwell were never a well known or popular axe in Oz. I'm not a bush worker, but some members of my family used to be, and I live in an area that has been a big timber getting area in the past. Probably Plumb was the Rolls Royce for a work axe, and usually 4.5 pound, a big man would sometimes use a bigger axe but I'd guess that more than 90% of work axes used by the timber getters in this area from the 1920's through to the present would be 4.5 pound. Of course felling was and is mostly done with saws, cross cut up till chain saws came into general use. Kelly and Hytest were always popular, but all I ever see in the hardware stores now are imported junk, not real axes at all.
This is what proper axes look like:-
http://www.osborneaxes.com.au/
http://www.tuatahiaxes.com/index.html