Check out my mod, SkyrimMC, which I am actually working on this exact system at the moment. Even though it is not complete, nor stable, it might do you good just to stay up to date until it is finished. When it is finished, I might as well just make the inventory feature a separate mod itself.
This is just personal preference... But I tend not to go for "I wish I were playing a different game" mods. The inventory in Minecraft is the way it is for a reason. And I'm gonna have to go with Entoarox. Weight limit in Skyrim is based off a strength stat, if not Feather equipment. You'd have to add stats to Minecraft and ways to alter those stats, in order to change how much weight you could handle. It'd also need an overhaul of how items are handled. The stack limit would have to be raised, but a new set of data would have to be added. The GUI of the player would also have to be editied to allow for scrolling.
Honestly, why not just play with NEI or creative mode? Or better yet, if you want to play Skyrim, just play Skyrim. Inventory Management is one of the core features of Minecraft, and I tend to find any mod that changes the feel to make the game less enjoyable. There's also numerous inventory-additon mods already made. Fill up on bags, and several of them even nest. You could have bags, full of bags, full of bags, full of stuff. Makes finding your stuff harder, but can give you that "limitless inventory" you're wanting.
Iguana's Tweaks tried to add "weight" by changing stack limits, as well. Maybe try that mod.
I meant like the Skyrim system of categorizing in a Skyrim GUI, not having Items ordered in the Minecraft GUI
Inventory Tweaks allows you to change the order of items. Just change the settings. It can't help you with the GUI, since that's part of the base game. I'm not sure I'd like scrolling through a list, anyway. I'm kinda used to my grid.