The OP has two intuitions:
(1) To say that something increases implies that it changes over time.
(2) It is OK to say 'y increases with x', when looking at x and y of different entities at one, given moment, so that no change in time is involved. (For example, 'wealth increased with years of completed education' can be a way of saying that the people who were better educated at the relevant time were also wealthier at that same time, without making any comparison to how they were earlier.)
Each of these intuitions is quite plausible, and yet, they seem to contradict each other. Is there a way to reconcile them?
There is. While in the cases described in (2) we are looking only at a 'snapshot', taken at one moment, and there is therefore no change over time in the subject matter, time is still involved in a way. These cases typically involve something that can be represented on a graph, and our reading of that graph takes place in time. Our eyes move from left to right, and, as they do that, we are looking at increasing x. In a particular case, we may notice that, as we do that, y is also increasing and express that by saying 'y increases with x'.
Of course, this wording can be used even when no actual graph is in front us, in so far as we are aware that the subject matter could be represented on a graph that would be read that way.
However, if nothing like that is the case, as in the OP's example of somebody's wanting to say simply that women are currently wealthier than men, increase is a wrong word to use. One can make sense of the sentence 'There was an increase in wealth among women compared to men' only if one takes the author to be making an implied comparison with their wealth in the past, in which case the increase in question would be an increase over time.
The account given here for increase also applies to change itself and similar words.