Does having lots of in-game items in Skyrim cause instability?

Basically, no. Collecting stuff in Skyrim is not "Forbidden", otherwise you wouldn't be able to do it. In terms of it affecting your file size and load times, it's too miniscule to make a difference.

However I'm sensing that your question is a bit deeper than that, and you're asking if your antics are causing issues in the game.

Depending on how many mods you currently have loaded in your game has a significant impact on the file size of your game. The more mods you have loaded, the larger the file size, and the longer the load times. I have seen reports of people running at least 160 mods, and the file size also being rather spectacular, so my suggestion would be to lay off a few quest mods that you don't play anymore.

Your file size has most likely absolutely nothing to do with it, although it's probably connected to the number of mods or more fitting, the lack of additional compatibility in your game files.

If you install or uninstall any mod, always run the programm "Loot" afterwards, it's free and it will organize your mod-order for you.

If you have install/uninstall a mod which adds items to vendors/enemy inventory, always create a "bashed patch" using the program "Wrye Bash".

If you install any animation mods, be sure to install FNIS (Fores new Idles) and use the "Generate FNIS Behavious for Users" tool.

Last but not least try not having multiple mods changing the same stuff (like multiple store overhauls for one location etc.), except when they're mentioned as compatible or when they're patches for it.

If you always do that you can easily run 250+ mods (I'm at ~270 now) without any problems or CTD's.