well..when there is a weak engine then there is not enough power in compression stroke, resulting in poor burning, usually due to worn out piston rings in turn damaging cylinder/chamber. rings help stop the oil come up to chamber and also help stop the fuel go down to oil sump.
when engine is too weak so oil comes up from oil sump to compression chamber and also accumulates in the spark plugs chamber. this is acute case.
Also with the passage of time carbon soot develops within cylinder. I always suggest use of synthetic oil for a new engine as it won't let soot/carbon residues stick inside the walls of cylinder.
All these things make life of battery and starter motor short.
Just to check ur car's engine is weak, in intitial stages, start it in petrol mode and have a look at the exhaust pipe, u might notice blue fumes which were unnoticeable while running on CNG. This is especially noticeable when engine is cold(hasn't attained optimum temp).
As far as fuel economy is concerned, yes, weaker compression means incomplete burning of fuel, wasting unburned fuel and of course less power generated by engine.
In this case one has to hurry and get the rings changed but overhauling an engine is not a simple idea, I've come across many engines having cracks in pistons or cylinder block but i am not suggesting not to change rings.
