I don't think this is right. My understanding is that the engine is typically the one of the heaviest dry parts of the vehicle and the fuel (at launch) the heaviest individual part overall. Especially nowadays since the electronics and sensors are tiny and antennae are lightweight.

This is especially the case with things like landers and geostationary satellites, where you want as much fuel as you can afford for station keeping, to keep the satellite operable for as long as possible.

Half of Nova-C's mass was fuel (~900kg), payload was 100kg. Starship's payload is ~100t, dry mass is ~150-200t but fuel mass is ~1200t.