The "operating" weight changes from airplane to airplane for the same engine. For instance ALL engines used oil so a long range plane needs bigger oil tank/s than a short ranged plane. They were ALL dry sump engines. Oil went through the engine, then through the oil cooler and then back to the tank and then to the engine again. Some planes might require bigger oil coolers than others, bomber doing a 20-30 minute climb at low speed but high power may need a bigger oil cooler than a fighter that climbs faster (less time climbing and with more airflow though the oil cooler due to higher speed).
The "dry" weight only includes certain accessories. Electrical generators and hydraulic pumps were often not included. Different sized generators could be fitted depending on the expected electrical load. Since the vast majority of aircraft engines used magnetos for ignition, batteries and generators weren't
needed to keep the engine
running. However electric propellers, flaps, landing gear and even cooling flaps might make having batteries and generators a real good idea
Same with hydraulics. the pump you need for a small fighter is not the pump you need for a big fighter let alone the pump needed for a multi-engine plane. And many twins did NOT duplicate accessories (pumps and generators) for both engines and LOTS of 4 engined planes only carried 2 sets of "accessories".
P-39s were "all electric", at least the early ones. NO hydraulics and an electric propeller. Some P-40s tried to save weight by taking out the electric starter and battery (or fitting much smaller battery) as they used hydraulic systems for landing gear and flaps and such. operating weight of each engine even if the basic engine was the same ? OK different gear box and drive shaft on the P-39 but you get the idea.
Gun synchronizers varied from plane to plane depending on gun installation as did prop controls, most used hydraulic propellers but some used electric and the pitch control mechanisms varied in weight. Please note the hydraulic propellers were NEVER connected to the the plane hydraulic system but used either engine oil or a separate oil supply and pump.
Some engines were even offered with several different starter options. Hand starters, electric starters, cartridge starters and combination starters (usually hand/electric). The "hand" and electric starters usually wound up a flywheel which, when wound up to speed, was clutched into the engine to turn it over.
Dry weight also doesn't include the exhaust system (usually) but may include the flanges and nuts the pipes are welded to or fastened with.
Liquid cooled engines
may vary from one installation for the same engine to another in radiator and coolant weight. And of course fuel systems can vary in weight even with no fuel.
Aircraft designer
knew what he needed for accessories and the likely weight of the accessories (or could look them up) for the plane he was designing. If he needed a 1500 watt generator (roughly 60 amp at 24 volts) then he needed that regardless of the what engine he chose and would figure the weight accordingly. Another designer working on a different plane might only need a 900 watt generator (40 amp ?) and lower the weight accordingly.
Throw in different engine mounts and cowlings and the "operating" weight of the same engine in different aircraft can vary quite a bit.