Why are AES keys increments of 64-bits?
When NIST made the call for AES, they were trying to address short comings of DES that had a 56-bit key (64-bits with parity).  I got the following information from NIST while at the NIST 8114 conferences because I was complaining about having to keep 192-bit key compatibility in my SIMON hardware when no one would likely use it.  

The summary:

In 1997, the idea was to double the key length (to 128-bits) and then double the key length again (to 256-bits).  The reason that 192 bits was there was because it was thought that an intermediate key length would be good for systems that couldn't handle the complete 256-bit length.  You need to keep in mind that at the time of specifying 128/192/256 bits, and algorithm had not yet been picked.  On 1997 hardware, 192-bits takes more time than 256-bits, and it was hoped that by having a larger key size the life of AES would be more than 20-years, unlike DES.

As mentioned in the comments, retrospectively, the 192-bit requirement was likely not optimal as pretty much no one uses it.  You have to include a 192-bit key option in your hardware cores for complete AES compatibility.  I had a bug in my netlist verification for AES-192 for 10 years, and I only found it recently, which really means... no one every uses AES-192.