Re: Ironic choice of picture at http://www.theregister.co.uk/data_centre/
First of all - if your backups are taking all weekend then you need a faster backup solution. If you are depending on incremental backups you're one broken tape away from being unable to recover data. If you can take a full backup every day and have that stored off-site that's much better, but few places can.
The problem with the Friday backup is that it assumes your tapes will be safe until collection on Monday morning. Northgate Information Solutions got this wrong. You will lose over a week's worth of data this way (and just in salary cost that could be a huge amount).
Early Tuesday morning means that the tape or backup device can be put in on Monday (which may mean going in on a Bank Holiday of course or putting it in on Friday - OK that negates the reason for doing it on a Tuesday but we only have four Bank Holiday Mondays per year most years) .
If a catastrophe hits your building on Monday night you will of course lose a week's worth of backups - but that's a risk spread over 16 hours not 64 hours. Since with only one or two possible exceptions Tuesday will be a working day someone will be in to take the tape offsite. If something happens to your building the following weekend then you've lost only 4 days worth instead of potentially 8. You might find Wednesday or Thursday to be a better idea of course - but Friday is risky.