i have made a thief before and i tried using light armour but i would get overencumbered when raiding house or cave and have to drop some good loot so my question is can unarmoured a viable option for a thief i dont plane to get into many fights and when i do i plan on backstabing or running

That should work, it may be worth adding athleticism as well to improve your running.

Remember that the amount you can carry is determined by your Strength. You might want to design a character with a bit more starting Strength.

Light armor is usually realllllly light, so it shouldn't have too much of an effect on encumbrance, unless you have really low Strength.

Also remember that Unarmored is broken in the vanilla game, so be sure to install the Code Patch.

well when i had a full set of light armour on my last thief it took up like half of the wight on my character and i had somewhat good strength oh and how is unarmoured broken?

I always start my thief characters as a Redguard, as their starting stats allow a slight advantage in combat and encumbrance. Also, using "Adrenaline Rush" as your default "fight or flight" mechanism when outmatched is a terrific boon.

Unarmored has no effect unless you're wearing at least one piece of armor.

If you are looting a whole cave, to avoid over encumberance, pile everything up in one spot . Pick it all up, recall to a town and sell. Once in town drop stuff on the ground and sell stuff. Come back to pile, pick up more and sell.