Will a static MySQL database become bigger in file size over time, even without anyone writing to it? I backed up a database a few weeks ago, then for comparison downloaded it again. It was about 10,000 kB larger. There should not be anyone writing to it, but there are lots of reads.

Will a static MySQL database become bigger in file size over time, even without anyone writing to it?
Back in August 2014, I answered this question : How to start mysqld with read-only data directory?
I mentioned how you could make the InnoDB Architecture completely read-only.
You can also read MySQL Documentation (Configuring InnoDB for Read-Only Operation)
The only reason ibdata1 would grow would be MVCC (needed to support transaction isolation). I wrote about such uncontrolled growth of ibdata1 in my post How can Innodb ibdata1 file grows by 5X even with innodb_file_per_table set?
Turning its features removes any need to write anything related to MVCC inside ibdata1.