Here's the numbers (which is more reliable than my anecdotal experiences):
The testing area was inside Solitude... from the arch in front of the Blue Palace to the arch in front of the training grounds that have that big red wolf banner hanging down. It is a straight shot down the path and does not require any movement from side to side to complete.
Naked : 27 secs : 0 total weight worn
Elven : 27 secs : 7 total weight
Glass : 27 secs : 13 total weight
Iron : 28 secs : 46 total weight
Daedric : 30 secs : 81 total weight
The tests were run in duplicate to reduce the possibility of measurement error, and are rounded to the nearest whole second.
As you can see, there is a slight difference in running speeds, but not a very large one. The daedric one surprised the most, as a loss of 2 seconds from Iron with not even double the weight makes it not seem very linear... but I'm not the math nerd, so take that with a grain of salt.

-Loth
Edit: Hilariously, the Conditioning perk for Heavy Armor
actually works as advertised, as when I repeated the daedric testing with the Conditioning perk, the time dropped to 27 secs. Obviously, getting the weightless perk for light armor (the name escapes me as I type this) will not do that much as far as speed goes, as the difference in running speed is negligible to begin with.