While they exert a disproportionate amount of guidance to other agencies, that is generally orthogonal to their primary motivations.
You can certainly make a case that NSA pushes NIST towards making guidelines for things that they favor, but I don't seriously believe that's at the expense of weakening other agencies (at least not as a goal).
As to classified and up information, the NSA can't get enough ECC, and many of the Suite B implementations of other standards are just a version of the standard that works (and is "certified") to use Elliptical Curve Cryptography (like TPM Suite B, which we work on).
Could NSA's hardware centric recommendations be motivated by an interest in leveraging economies of scale (due to the size of federal IT procurement) and purchasing COTS hardware that was optimized for AES?
On a related note AES is the NIST standard for protecting sensitive but unclassified information:
"Applicability. This standard may be used by Federal departments and agencies when an agency determines that sensitive (unclassified) information (as defined in P. L. 100-235) requires cryptographic protection.
Other FIPS-approved cryptographic algorithms may be used in addition to, or in lieu of, this standard. Federal agencies or departments that use cryptographic devices for protecting classified information can use those devices for protecting sensitive (unclassified) information in lieu of this standard." [1]
I have always assumed that this scope limitation within FIPS197 meant that NSA, DoD, Secret Army of Northen VA, etc had a different standard/requirements (NSA Suite A&B) for classified (and up) information. Is this the case? If so why would NSA have so much skin in the game if they were not restricted to FIPS197 requirements?
[1] http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf