Notice helicopters always have engines that can produce as much thrust as they weigh. If I'm wrong on this, please correct.
The helo's "engines" (by this I surmise you mean the turbine/s, gearbox, and rotor) create
much more thrust (actually lift, since it's vertically oriented) than they weigh. The excess lift carries the fuselage, landing gear, fuel, payload etc. plus some margin for maneuvering.[I]
And just to show that the basic fundamentals of lift are really no different from airplanes, Helos are oft referred to as "rotary-wing aircraft", vs "fixed-wing" for conventional planes.