A person who talks about how good they think they look seem to need to hear that they look good.

The simplest way of dealing with people is giving them what they want, unless it is too costly in some way.

It is very simple to give this person what they want - confirm that they look good.

Your reaction - complimenting less - seems paradoxical and irrational. They want more compliments, and you are providing fewer compliments. Why?

Go with the flow unless it is too costly. In this case, it is not too costly - they just want compliments. Not a house in Beverly Hills, but just compliments. A trivial request which should be satisfied without further analysis.

Also, to the extent that the person wants compliments, but you are intentionally withholding compliments, you are not being generous in this r/s. Not being generous in r/s is unappealing. Try to be more generous. You might even find yourself being treated better by the partner.