In that example, it is ok for A and B to get equal share - if you are measuring unique users and not usage. There is no inflation here, at least not in the methodology, which looks like a valid statistical one to me.

Of course it could be wrong in practice, if the data used to re-weight is misleading (while the unweighted raw data was more accurate). That's possible in theory, but seems less likely - there is fairly good information about internet usage in general which is what is used to re-weight, certainly compared to browser share.