Well-fitted rigid armour distributes weight quite well, but mail typically puts a lot of it on one's shoulders.
Having made and worn my own mail[1], it's a bit more subtle than that. It moulds itself to the wearer in a way that even cloth does not, and weight is largely borne by
all upward-facing surfaces over which it is draped, which is (in an upright position) all the way from the end of the shoulder-joints to the neckline, on both sides, and significant parts of the extreme-upper chest/back take on a proportion of the load. Which makes it less 'oppressive' than rucksack straps, even for the same weight. (And it does this better than fully rigid armour, accommodating all kinds of flexibility, although good plate armour is designed with shifting-plate flexibility around that area that, together with the padding, somewhat rectifies this.) When you lean forward, the weight spreads its way along your back, and if you're on your back then the weight (which is now not even counting the mail that is now supported by the floor that you are laying on) is spread across your front. Etc. Of course, if you're wearing the more 'dense' 6-1 or 8-1 linked mail, it sure makes for a whole lot of weight, and I've never worn it in
actual combat.
The worst thing about mail(le), IME, is that the inherent slack in the 'hanging' sections has its own inertia when you move around. Ideally, its own weight, hanging down, closes up the rings in the horizontal direction (this might depend on which way you've 'knitted' the rings, but it applies to some extent or other both ways) and reduces this, but at the lower fringes you certainly feel like a flamenco dancer if you spin around fast enough and it's your top layer of protection so lets itself spin outwards...
[1] Not /strictly/ authentic, but close enough for comparison.