In a turbojet aircraft with two engines, when one fails does the weight of the working engine increase due to the fuel flowing to it? If it does, how is the weight balanced on the failed engine side?
Since your question is specifically on "jets". We need not worry about the critical engine.
There is one thing to be noted in most of the commercial jets. The engines are placed close to the fuselage in order to reduce the moment arm - mean that should an engine fail, there is a reduced difference in forces,as compared to if an aircraft had engines on the wings tips.
The following are two vital things to be carried out during imbalance due to engine failure:
1) Effective rudder (and aileron) control:
The rudder (and aileron) is used to maintain directional control in flight, acting around the normal axis. An engine failure will yaw (and roll) an aircraft, making the rudder (and aileron) the best control to counteract this.
2)Fuel Balance procedure:
Detailed schematic of a B737 Fuel System:
The procedures vary from one aircraft to another. And for a turbo prop aircraft it's a whole new thing involving "critical engine".
Fuel systems are designed such that when an engine fails, fuel is no longer supplied to that engine. Further, fuel can be supplied from the tanks(s) on the failed side to the operating side to maintain balance as the operating engine continues to burn fuel. The details of how this is done and the extent to which it is automated depends on the aircraft type.