The throttles on the 2V K bikes don't tend to "snap back" like they do on many motorcycles. After trying different approaches to "cure" this I finally found a solution to this minor inconvenience.
The first thing to do is to make sure that your grip rubber isn't rubbing against the side of the throttle perch.
The next thing is to clean all of the old grease out of the throttle gears next to the master cylinder:
a) Remove the Phillips screw near the bottom of the right combination switch to remove the switch from the throttle perch. Be sure to use a good screwdriver with appropriate pressure as that screw can be sticky and it's easy to strip the head if you're not careful.
b) Remove the large black Phillips screw (7) to the right of the master cylinder reservoir. Once that screw has been removed the plate (8) that it holds down can be removed. This will expose the throttle gears and allow the throttle tube to be pulled back.
c) Clean out all of the old grease in the throttle gears and on the throttle tube gears.
d) BMW recommends that these be regreased with fresh grease but what I've found works well is spraying the cleaned up gears with a bunch of 3M spray silicone lubricant. It's a much lighter and thinner lubricant which doesn't impede the movement of the throttle as much as a thicker grease does.
e) Also spray down the handlebar under the throttle tube with the silicone lubricant.
When you put everything back together you'll find that the throttle will "snap back" much better than it ever has.
