You are finding that individual files larger than 3.99 GB are failing when you copy them to a USB memory stick (or a camera memory card, or an external hard drive).
The simple answer is that the memory stick is formatted with FAT32 formatting. http://en.wikipedia.org/wiki/File_Allocation_Table The File Allocation Table method of formatting limits an individual file to 4 GB less one byte, because it cannot store a longer file length entry. So no individual file can be over 4 GB in size, although the volume can be larger. Windows puts an arbitrary limit of 32 GB that it will format a FAT32 drive volume to, but a FAT32 drive can be formatted up to 2 TB with a standard sector size on a Mac or with third party software.
The solution is to reformat the USB stick (note that this will erase all the data on it, so back it up first). On a Windows machine, reformat it with NTFS. On a Mac, reformat it to HFS+ (Mac Extended). The downside of this is that devices like media players, smart TVs and cameras will probably not be able to read the stick – they require FAT. Also, Windows machines can’t read Mac Extended, and Macintosh machines have a limited ability to read but not write NTFS.
Newer cameras and camcorders with high capacity SD and CF memory cards (64 GB and higher) use the exFAT formatting method. exFAT is supported in Windows 7 and higher and OSX 10.6.6 and higher. Patches are available for some older Windows OS versions. http://kb.sandisk.com/app/answers/detail/a_id/3389/session/L2F2LzEvdGltZS8xMzM4OTI1Mjc3L3NpZC9nRmhVeFdaaw%3D%3D