How do I tighten up a manual mirror

Rather than glue, in the old days we used to put a small hose on the end of a tube of silicone caulk. Slide the tube under the glass till we felt it hit the plate and ball, we then just pumped some caulk in and let it setup. Most of the time it would tighten it up enough to not droop but still move somewhat if need be.

If it is a brand new Mirror I would send it back, that's just me though.