Advice please, for IKEA (hopefully okay to ask here)

I need to put up kallax cabinets because I'm a clothes horse, I'm not allowed to attach them to the wall. The owner doesn't want to deal with drill holes.

I'm thinking of mounting something heavy to the back because I'm afraid of it falling over. I haven't put it up yet. It's only going to be clothes so maybe I won't even need to?

If I do what is best to do? A sheet of metal or square weights on the back or put on top.

Thanks for any help