Just wondering, I made the chest in the Riverwood Inn room mine because I'm always there.

Pretty sure not. It'll still respawn. And that's what you have to disable.

Is there a command to stop it from respawning then?

I don't know. Pretty sure you need the Construction Set to edit that.

y do this when u can just get a room from any of the factions or the college. or just buy a house. 5k for the whiterun house is cheap.

I'm roleplaying and my character is planning on staying in Riverwood for quite a while, another 1-2 in-game week at least.

A storage there would be nice !

If you dont mind using the console then just use player.modav carryweight 500 (or whatever you want to give your character) to increase the amount of items your character can carry.