Do snap files get larger?
I noticed with disc analyzer that my disk free space is gone down from 974 GB to 971 GB over time on system updates and my snaps folder went from 1 GB to 3 GB.
Do system snaps get larger as system updates get newer?
Old versions of snaps are retained by the system but you can remove them and control what goes on behind the scenes.
The default number of versions retained is 3 but there is a snap option to use in terminal to reduce that to 2:
sudo snap set system refresh.retain=2
and you can write a script to remove old snap revisions.
This reference shows you how.