Running a 64-bit O.S. on a 32-bit CPU?: that doesn't seem very likely to work.
Not all Acer Aspire Ones have 32-bit only CPUs. The Acer Aspire One 722 has an AMD C-60 in apparently, which I know for two facts is a 64-bit capable CPU, the second of which being that I have another customer's laptop sitting at home right now running Win8.1 64-bit.
Having said that, the OP's machine might only have a 32-bit capable processor, the Acer Aspire One label has been around since something like 2008 or 9 I think, which might put it in early Intel Atom territory (which was definitely 32-bit only).
However, considering that the OP says this one is running Win7, it has to be newer than late 2009 (unless the OP upgraded it).
@ OP
The laggy text issue doesn't seem right even for that class of processor. Is this when you're doing say a Google search or even when you're typing into the plainest of plain text editor programs?
Can you provide the exact specs of this netbook? Have you tested the storage system for any hardware faults?
I encountered an early Aspire One with an Atom CPU in which had a storage system in that was so slow that I think an SD card would have given it a run for its money. I think technically it was an SSD but it worked more like an ancient flash drive running on USB 1

IIRC OpenOffice took something like an hour to install on it.