Lowering weight penalty for heavier armor would increase the speed of infantry, causing them to close on the archers sooner. When they get close enough, the archers will just start running. Seeing as how alot of archers have the same if not more ath then infantry, they will be able to run away still, but not as fast.
Maybe if this was coupled with a longer period to reach full speed, then it would fit its intended purpose better.
Edit: oh ya,forgot about the second part. Sheathing the bow does not take long. With ur suggestion, archers may not be able to take pop shots, but can still run long enough to get enough range between his chaser to unsheath, take a shot, sheath again, and run away.