Why are LiteSpeed or Native differential backup files growing larger in size? (4223101)

Differential backup files growing larger in size each time a differential or translog log backup is completed?

Because a differential backup will backup all the data that has changed from the last full backup.
For instance, a FULL is scheduled every Sunday. Friday differential backup probably has more changed data and be larger in size than Monday differential backup. Why? If you change the same exact data over and over again, a differential backup should stay about the same size regardless if you take the backup today or several days from now.
On the other hand, if users modify/add different data, the size of the differential backup will continue to grow until you take a full backup.

Take a FULL back up of the database.

Other points to research on this topic:
1. Backup the Differentials the WITH INIT option. Since differentials always begin from the last full backup there is little or no need to keep previous differentials.

2. Is the database in simple recovery model?
if yes --> there are probably transactions that are still uncommitted
if no --> you need to truncate the log before shrinking, in simple recovery model, upon committing the transactions in the log file, the 'space' gets freed up

3. You may wish to look into BACKUP LOG WITH NO_LOG (or a normal backup) and then DBCC SHRINKFILE?
It is not recommended to backup log dbname with truncate_only because you would be losing data.

The detals of these processes are available at Microsoft's TechNet website.