Remove any electrical power from the oil burner. If necessary, shut the circuit breaker off at the main electrical panel for added safety.
Remove the back panel of the Weil-McLain oil burner by detaching the screws with a screwdriver.
Search for the fuel oil pump within the burner's assembly. In addition, visually verify that the oil valves within the burner are set to the open position for a free flow of oil to all parts of the appliance.
Open the intake port on the fuel oil pump, using a wrench.
Observe the intake port. Air should be bleeding out of the oil lines at this point. Allow the port to remain open until oil begins to leak outward from the opening.
Soak the excess oil up with a rag. Reattach the port's cover with your hands and tighten with a wrench.
Reverse steps 1 and 2 to reassemble the burner. Turn the Weil-McLain oil burner on and verify that it is emitting heat normally.