When I went through U.S. Air Force tech school for the APQ120 airborne fire control radar (some 35 years ago), our very first classroom lecture was on RF hazards and safety.
The biggest health threat wasn't being "cooked" but rather the danger of subtle but potentially serious long-term damage to the lens and retina of the eyes - especially if one knowingly or unknowingly looked right into the boresight of an energized antenna.
The "danger zone" was considered to be within 40 feet directly in front of the aircraft. We were told that RF-induced damage to the lens of the eye might take years to manifest - typically in the form of cataracts. (At a much younger age than one would normally expect such a problem to develop.)
Granted, the APQ120 peak power output was far higher than anything you would be likely to encounter in a modern weather radar.
Also, one should be careful around belly-mounted transponder and DME antennas when working around an aircraft with electrical and avionics energized. On most large aircraft, these systems won't actually transmit with the weight on wheels, but that is not always the case.
A typical high-end transponder like a TDR-94 can produce close to 1000 watts of peak RF power, and if there is an operating ATC radar with interrogator at the airport, (and the transponder control head is not in STANDBY mode), it's quite possible for the transponder to be generating replies every few seconds anytime the aircraft and avionics are powered.
JR Barrett