I would like to make a mirror with a timber frame weatherproof

I don't know how to make it weather proof, but to make it weather resistant remove the mirror and coat it with several layers of outdoor polyurethane.

To make it withstand weather better - spray with polyurethane. But I would take it inside during the winter.

What the previous poster said. Also, there is a varnish for teak, I think, that sailors use on their boats but I can't remember the brand right now. That might work on the frame.

I would go with a marine poly, give it a number of coats on every inch of the wood to make sure you have less vulnerable areas. The marine poly is made to protect the wood on boats that see hot, humid and all the elements. This should protect it for years to come.