In case you were wondering if you want to get a backup for your ever-evolving stats and records on your Modern Warfare profile, you should rest easy.
But if you still insist, the location of your profile is here "C:\Program Files (x86)\Steam\steamapps\common\call of duty modern warfare 2\players"
Modern Warfare 2 Profiles are stored online, thus, unneding anything to backup.
So if you feel the need to format your pc or if it crashes, you can still retrieve your stats by just reinstalling the game and singing in to your steam account.
Notes:
There are glitches that can prevent you from overwriting your profile stats even when you play online. If you use deep freeze and update to a newer version, your stats before the deep freeze point will be preserved.
Click here if you are looking for COD4: Modern Warfare PC profile backup