How to calculated weighted gain of antenna?
I did not know this specification and I also think it must specify the weighting function or it is incomplete (Can you provide a link to the document?)

But I’m pretty sure it is meant to be a simple mean value: You must calculate the mean value of all S21 data points within a certain bandwidth. 

Attention: It is not correct to build the mean value of the LOG values, instead you must convert your datapoints to non LOG values first. 

The average is declared as the nominal gain of your amplifier, so it is different from the weighted gain of the S21 data points (mean value).