Remember it's up there when you move house!!

I would be getting good qual sealed tubs, not boxes. Boxes are mansions for critters. Also, think about what you're storing & whether it might degrade as a result of extremes of heat/cold. For eg, you shouldn't be keeping photos & negatives up there.

Also, think about the weight. It's not safe to store heavy items in high places (greater risk of dropping it in yourself).

PS stuff shouldn't get sweaty unless it's damp/humid when you pack it