SQL Server Backups - A couple of questions

We run our weekly backup job at 9pm on Fridays and we are experiencing a couple of issues with regard to disk space (which gets perilously low at times) and performance. We're looking at streamlining/optimising what happens and would appreciate your comments.

Specifically:

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The backup process is taking about 4hrs to update statistics during
the backup. Can we safely disable this process to save time?

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We're running low on disk space very regularly and wondering if we should re-jig the process. Currently it creates the backup and then deletes the previous backup and this is what is hogging disk space. Can we safely delete the previous one first and then do the backup?

Any other comments or observations would be very welcome
EDIT: Total size of SQL files on the server is around 35GB. One db is about 25GB in size while the other six share make up the other 10 or so GB.

(1) Yes, I usually have the backup process by itself. I would not be doing much of anything during my backup time if I can. You might have it take the backup and then do the update on stats. As it sounds it seems you are running two jobs (1 for backup, 1 for update stats) at the same time?

(2) Do you copy the backup to tape or other disk storage? If so then I usually clean up the files before I create new backups locally. If not, then if I am scraping for storage space I would consider zipping the backup file prior to the new one being created. (That is if you cannot enable compression on the backups, as @Simon suggested, this would save some space as well.)

StackExchange Database Administrators Q#6431, answer score: 8