The "weekly backups from several years ago" will disappear. The Time Machine Preferences window points out that "The oldest backups are deleted when your disk becomes full."
After doing a backup, I think that's when TM checks through to see if there are hourly backups older than a day that should be removed (the first is kept as a daily?) and if there are daily backups older than a month that should be removed (the first daily in a week is kept as a weekly). So some snapshots are removed at that point.
When TM is about to do a backup, it works out an estimate of how much space it will need on the TM volume. If that much space is available it goes ahead. Otherwise it goes into a cycle where it deletes the oldest backup and checks again how much space is available.
Note that an old backup might not actually be taking up much space: only the data that is changed between it and the next-oldest backup. So if you put a huge amount of data on your disk, the next TM backup could take ages while it deletes lots of old backups, gradually getting enough space.
I have seen situations where ALMOST ALL the TM snapshots were removed in order to make space for new data. Admittedly this isn't always the action you want, but the bottom line is that TM gives priority to newer data. If I know I'm shuffling temporary data I either put it into one of the folders I've told TM to ignore (e.g. I have a "tmp" folder under my home dir for this) or I temporarily turn off TM.
If you've put many GB of data onto your system temporarily and TM included those in a series of backups, then eventually when the last of those are old enough to be removed (either because they were just hourly or daily and didn't make it into a weekly snapshot, or because they're in a weekly that's getting removed in search of new space) then when that last copy is removed the free space on the TM volume will take a big jump upwards. Until then they'll just sit there chewing up space.
