I know many players will choose just to eliminate any restrictions on amount of loot carried, or at least to vastly increase the allowed weight.

For me, those options feel too much like cheating. I would appreciate some more modest aids though. Some potential ideas:

1. Give my main character any unused weight quota from my companion. For example, if Lydia can carry 100 more pounds of stuff, just give me that extra capacity. There is nothing fun about handing over 1 item at a time between us.

2. Give an option for item menus to be sorted by "richness", which is item value divided by item weight. Will make it much easier to spot the clunkers you didn't even mean to pick up like the "Stupid Rusty Chest Plate" that is worth 2 gold but weighs 50. Will also help you to sell the clunkiest items first, when dealing with vendors who don't have enough gold to buy all your loot.

3. When picking up a new item that puts you over your weight quota, optionally auto-drop the new clunkiest item. Of course don't drop anything that is equipped or favorited. (This one would probably need some tweaking to be workable and even then I'm not sure its really a good idea.)

If I could see my inventory list sorted by weight (either per item weight or total weight of stacked items) that would also work. I mean, I should be able to feel how heavy things are, no?

Another variation would be if I could see items sorted by when I picked them up. Even if it's just the last few items I picked up, I should know what those are.