See if the following notes taken from Apple support page are useful to you.
As your backup drive begins to fill up to its capacity, Time Machine intelligently deletes the oldest backups to make room for newer ones (and will alert you if the “Notify after old backups are deleted” option is selected in Time Machine preferences).
If your backup disk is filling up often causing your oldest available backups to be erased sooner than you might want, consider the following options:
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Use an additional drives for your backups or transfer your backups to a new, larger drive as detailed above. When you connect a new drive for the first time, use Time Machine preferences to select the drive. Tip: You can also browse the original backup drive for past backups by using “Browse other Time Machine Disks”–to see this choice, hold the Option key then click the Time Machine menu in the Finder (to see the menu, “Show Time Machine status in the menu bar” must be selected in Time Machine preferences.
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Reduce the amount of information being backed up by adding to the “Exclude these items from backups” list in Time Machine preferences, as mentioned above. Your backup drive will fill up less often.
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Delete file(s) that are no longer needed (such as from your desktop, Documents folder, or other Home folder locations), so they will no longer be backed up. You can also enter the Time Machine restore interface and find files that can be removed from the backup drive itself to conserve space. To do this, select the file(s) and from theAction pop-up menu (gear icon) in the Time Machine Finder window choose “Delete All Backups of…”. Be sure to only delete files you are sure you won’t need or want to restore later.
