Were the both liquid- and air-coled paying same weight penalty for HP delivered?
It comes out close. The air-cooled doesn't have the radiator of course but then most air-cooled engines didn't quite get the same HP per pound that the liquid cooled engines did (dry weight). This, of course, bounces all over the place as different models and boost limits are used. A few pound per HP figures.
Wright R-1820 at 1200hp-----1.10lbs per HP
P&W R1830 at 1200HP -------1.22lbs per HP
Allison V-1710C at 1090HP----1.23lbs per HP
Allison V-1710F at 1150hp----1.14lbs per HP
Allison V-1710F at 1325hp----0.99lbs per HP
Packard V-1650-1 at 1300hp-1.16lbs per HP
Merlin XX at at 1480HP-------0.98lbs per HP
Wright R-2600 at 1700HP-----1.16lbs per HP
Please note the weight penalty paid by P&W by going to a two row design for the radial. They do get a smaller frontal area though
Air-cooled engines almost never got a WER rating without ADI.
Some figures for engine installations. numbers are pounds per horsepower.
engine.....................................1.000-1.300
Propeller and controls.................0.300-0.350
Engine mounts..........................0.045-0.080
Cowling...................................0.063-0.100
Exhaust system........................0.027-0.087
Carb. air scoop.........................0.015-0.025
Oil system (empty)....................0.040-0.060
Fuel system (except tanks).........0.020-0.040
Starter....................................0.020-0.045
Generator................................0.025-0.035
Misc.......................................0.015-0.030
radiators and coolant.................0.200-0.280
Increase over single stage supercharger
Mechanical drive with inter-cooler..0.150-0.250
Turbo with ducts, intercoolers etc..0.300-0.400
Liquid cooled engines tend to be at the lower end of the Lbs per Hp ratio to begin with (when the Allison was giving 1090hp the R-1820 was usually rated for 1100hp and the R-1830 was 1050-1100hp), they usually needed smaller cowls and perhaps smaller oil systems/coolers. Most V-12s used simpler exhaust systems than most radials.
This chart is from "Aircraft Power Plants" by Fraas, 1943 and is for engines between 1000-2000hp.
Exceptions can always be found.