Cheap uN Force sensor
One of the options is to measure something else, e.g. use lever system to move feather-light shutter over light sensor, or magnet on a long arm next to hall sensor, or beam of light deflected by the movable prism etc.

Note that the last one can be made practically friction-less, and the sensitivity is defined only by the length of the beam, so you can make extremely sensitive device for very little cost.