SUGGESTION:
Make Light Armor Run Speed: Fast
Make Medium Armor Run Speed: Normal
Make Heavy Armor Run Speed: Slow
NOTE: The variation in run speed only needs to be a slight difference between each other to give the lighter armor types more utility.
FOLLOW UP:
I play PVE mostly. Perhaps a PVP player can chime in on this too:
For PVE, light and medium armor are basically useless. The advantages/disadvantages of each make it clear that heavy is the best option. Everyone on my server gave up on light and medium armors and now use heavy armor exclusively. I have a mod installed to skin whichever armor they want so they can still have the light and/or medium armor look.
Yes, there are some advantages/disadvantages to each armor type now, but adjusting run speed of each would greatly raise the appeal of light and medium armors. Lowering the run speed of heavy armor would have some reconsider heavy so not everyone just defaults to heavy.
It only makes sense too. You would walk and run slower in heavier armor.
Food for thought. If this has been suggested before, my apologies for the duplicate suggestion. I did not see this suggestion made during my quick search of the subject.
Cheers.