Most people think of cancer or radiation poisoning when they hear "radiation." However, these hazards exist only for ionizing radiation of extremely high frequency (x rays, cosmic rays, gamma rays, hard ultraviolet), and not non-ionizing radiation at the far lower frequencies used for radar systems and microwave ovens.
The effect of radiation from radars and microwave ovens is mainly diathermy—that is, its main effect on human tissue is to heat it up, just as a microwave heats up food. The degree of heating depends on the frequency and intensity of the radiation. Excessive heating can cause tissue damage and degenerative changes, but not cancer or genetic damage. (Cancer and genetic damage generally require that molecules and atoms be torn apart, which non-ionizing radiation like radar isn't strong enough to do.) In rare cases of direct exposure to microwaves from ovens (obtained by disabling the interlocks on the doors), cases of internal burns have been recorded. Also, exposure to intense microwave/radar radiation can cause cataracts in the eyes, because they are very sensitive to heating, since they are not directly cooled by blood circulation (the same thing that happens to the white of an egg when it is fried).
The long-term effects of low-level exposure to microwave and radar radiation have not been quantified or identified to any extent, and remain the subject of speculation. It seems logical and prudent to avoid exposure to weather or other radar to the extent possible, but occasional exposure probably won't have any measurable effect.
I'm reminded of one of my relatives, who worked on very high-power defense radars many decades ago. He and his buddies found it amusing to sweep the radars across office buildings because they were powerful enough to light fluorescent lamps in the buildings, and they sometimes stood in front of feed horns of the radar systems with lamps in their pockets that would light up. The radars could also set off old-style one-use flashbulbs by inducing currents in them. Despite the obvious heavy exposure to radar radiation that this all implies, neither he nor any of his buddies has ever suffered any ill effects, and after sixty years, if something were going to show up, it would have done so by now.
Note that using a cell phone exposes you to the same type of radiation used by radar and microwave ovens.