Well, beyond realism, weight/space restrictions are typically there to force the player to make choices - you can’t carry your entire axe collection with you (including the +3 brown tundra bear slayer (bonus only applies from 9 to 5 during mating season)), and it’s up to you to decide, from the humongous list of shit you’ve pilfered, hornswoggled, right-of-conquered, “found”, swindled or otherwise acquired, what to bring on your Hero’s Journey. Take it far enough and you end with something like JESawyer’s New Vegas mod (as well as the umpteen “survivalist edition” mods out there) where every pound carried had better be useful, because that’s so many medkits, bullets, food, water and radiation meds you’re not bringing along.
In the context of the TES system more specifically, I’d wager it’s also there so that your character can’t compulsively pick up every. single. item, from tin cutlery to mid-sized beds ; which would likely eventually crash the game just keeping track of where all that shit is and keeping it in memory at all times.
But I’d say the most important role It (and the gold limits on merchants) serves is delaying the point where money just stops mattering. It’s not that money doesn’t help or doesn’t have any uses at all - it’s just that soon enough you have enough money that you could straight up fricking *buy *Skyrim from the Thalmor. That’s true in every RPG - money is always just an early-mid game concern, while late game it’s the sheer scarcity of upgrades that bottlenecks the player.
Now, if you can’t carry every last item you find, and you can’t sell each item for a bazillion gold, you stay poor longer. Which means you can’t buy all the grand filled soulstones, all the crafting materials, all the homes, all the rare alchemy ingredients etc… straight out of prison. End result is a delay of that I-could-just-buy-Skyrim phase, and more “choice” (in that you get to ponder what’s the best buying order for all that shit you know you’ll eventually own come endgame).
ETA: it also forces you to keep your priorities straight: yes, you could take three hours making trips back and forth from that draugr pit to sell every last rotted linen in there, milk every last gold coin out of your conquest. Or you could go and conquer somewhere else instead. Your choice.
Compare to, say, Daggerfall, where not only did merchants have unlimited gold, they would also dutifully buy in the morning the very items you’d stolen from them during the night - by just staying inside past closing time. Although of course, there was an even easier get-rich-quick scheme: travel to some dinky out of the way nowhere province, stroll into the bank, take out a loan of eleventy billion gold, skip town and never come back. Presto, zillionaire right out of the starter dungeon. Talk about easy money…
