This is not unusual at all.
The log size is related to the amount of activity, not to the DB size.
Some people have a log size bigger than their DB, some do not.
It is not uncommon to have TSM logs > 5 GB!

The simple thing, just make the log bigger.

Here's another idea you could try:
Create a devclass with TYPE=FILE (goes to disk).

Schedule an admin command on the weekends that does a DB backup with
type=incr, using the TYPE=FILE devclass.
That can run with no operator intervention, and will clear your log.
Then on Monday you can go back to your DB backups on DLT.

So :
on Friday       DB BACKUP TYPE=FULL to DLT devclass
on Sat          DB BACKUP TYPE=INCR to file devclass
on Sun          DB BACKUP TYPE=INCR to file devclass
on Mon          DB BACKUP TYPE=FULL to DLT devclass