TL;DR, latest Steam updates introduced a memory leak with the steamwebhelper.

I reported this issue back in July, when it first appeared in the Steam Client Beta, but it was ignored, and has since made its way into the stable release. At the time, the issue was able to be mitigated by removing oneself from beta participation, proving that it was a change in the client causing the issue.

The issue seems to be related to the library page, as the web helper instance that ultimately ends up using multiple gigs of ram is the one running the library. When memory usage starts to get to ridiculous levels, the library page stops functioning correctly, and terminating the process causes the library page to reset.

In addition to my previously ignored report when the issue was first introduced, I contacted Steam support, and was told to try clearing the web cache, which had been predictably unhelpful. The remainder of the message was "We can't help you now, wait for update, post in forums."

So, no, I don't think anyone will be able to help with this, but it needs to be known, and it needs to be shared.

EDIT: I've turned off GPU acceleration for webviews to see it that changes anything. In a day or two, I should be able to tell if the memory usage is still continually increasing.