Assuming it is a USB drive, you might want to test it:
http://www.pcworld.com/article/2455205/test-the-speed-of-your-usb-drives.html
That's where I was going too. Check it out, as per that link. Also, try a different USB port on the Acer Aspire, and check any settings through device manager and BIOS that might have USB ports set/limited to operating at USB 1.0 or 1.1 speeds.
Also, what back-up program are you using? Some have settings limiting the amount of CPU they'll use - see if there's such a setting and (assuming your running overnight), let it have 100%.
Is anything else running that would conflict with it? Have you tried to temporarily disable whatever anti-virus / anti-malware you're running?