I was using version 5.1.15
It updated to 5.1.16. But not to 5.2
What should I check?
This is the standard behaviour for Wordpress 5.1. WordPress didn't automatically update to major versions prior to 5.6 (5.2, 5.3 etc. are major versions). You were updated to 5.1.16 because a security update was just released and those are often back-ported to previous major versions so that they can be applied without updating to a major version.
The official documentation on automatic updates, and how to control them, is available here:
It's also worth nothing that 5.1 is 11 major versions behind, so I would advise updating as soon as possible.