The file size limitation of FAT32 has nothing to do with external drives or how Disk Utility did the formatting. It is a limitation of the older file format; if you use the Windows PC to reformat the drive using FAT32, Mac OS X would have the same problem. If you used +Mac OS Extended (Journaled)+, there is no file size limitation, but Windows cannot read or write the Mac format. If you used
NTFS (the newer Windows format), it would have no problems on a Windows PC. Mac OS X can read NTFS, but it cannot write it.
Is there a way that I can increase the size that is allowed to transfer?
Not if you use FAT32 formatting on the drive. However...
There are third party drivers that can make NTFS read/write on Mac OS X. I have no experience, but you can search using Google on +NTFS Mac+. The reverse option is to use MacDrive on the Windows PC, which is supposed to make +Mac OS Extended (Journaled)+ read/write with Windows.
If the two computers are on the same local network, you can also do the transfer through File Sharing.