Maybe this will help.
I looked at the number of BUILD_LOG tokens on the help screen, and found 366 of them, with the size of the frame about 2.3MB.
After Jenkins is restarted yesterday evening, there was exactly 1 BUILD_LOG token.
After running 8 overnight jobs, there were 30 BUILD_LOG tokens.
After running 2 more jobs, there were 37 tokens.
One more, there were 41. One more, and it is 45. One more, it is 49.
A run of a job adds 4 more sets of tokens to the help screen. However, the 8 overnight jobs produced 29 new tokens, which appears more like 7*4+1. Also, the first 2 jobs in the morning produced 3+4 tokens. It might be worth to notice that the morning project was brand new, with the first job being the very first run of it.
As you asked, I'll upload the config.xml for one of the jobs that ran overnight.
The relevant installed plugins are: