If a double backup is not desired then the following two options are available:

1. Disable Checkpoint Restart
Note: Failed Job in this case will need to be rerun manually. 

OR

2. Exclude the Weekly Job run from the Backup Schedule that clashes with the Monthly job.
For more info see:
Backup Exec Administrator Guide : Excluding dates from the backup schedule for all backups

 

 

 

Checkpoint Restart (CPR) is a Backup Exec feature that enables Backup Exec to automatically resume a failed job and restart from the point where it was interrupted after waiting the specified interval.
Only one job in a job family can be automatically resumed at the same time and another job can run whenever possible. Backup Exec, by default supersedes the less frequently running job if there is a scheduling conflict. Example 1:
Daily backup job (runs everyday), Weekly backup job (runs once a week), Monthly backup job (runs once a month) are all scheduled to run at 11 pm.
At this set frequency, Backup Exec supersede rule will run the less frequent scheduled job. In the above example; the Weekly job supersede the Daily job and the Monthly job supersede the Weekly job.

If Checkpoint Restart is enabled the behavior described above changes:

Example 2:
With Checkpoint Restart enabled, if the Monthly backup job runs into some error, it will be rescheduled to run accordingly to the Checkpoint Restart Error Handling rule.
In addition, during the CPR job restart wait time, the job that was paused by the job superseding rule, as described in Example 1, would start to run. This is to ensure that at least one of the two jobs will be successful.

This means that the earlier superseded Weekly job will run and so does the Monthly job which would be scheduled by the Checkpoint Restart rule.

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