It wasn’t so much a weight issue as the fact that rubber (for tyres) and fuel was in chronically short supply by the time the Komet was being deployed.
Most of them just sat on the airfields for lack of fuel, and by the end of WWII even ME-109s and FW-190s were being deployed with wooden tyres because there just wasn’t enough rubber available.
So re-usable rubber tyres for take-off, with a wooden skid for landing, was actually quite a sensible design choice a the time (especially given the Komet’s quasi-experimental nature), meaning they could use (and re-use) the same set of tyres for several aircraft.