Interesting topic. I can't really shed any expert knowledge here, but this sort of thing would be right up Doug Ritter's alley, if he has the time and inclination to respond.

Just off the top of my head, I would say that any time you fly in a light, private aircraft the risks are astronomically higher than in a commercial airliner, so to be absolutely safe, you would avoid all private aircraft. If that can't be done, personally knowing your pilot and his long reputation as a safe and proficient pilot would help. And barring that, It would be wise to at least check the weather forcast yourself.

You won't be able to analyze the weather the way a trained pilot can, but you can at least have an idea if severe weather is forecast. You can use this information as the basis of your decision or you can discuss the weather forecast with the pilot and use the discussion as the basis of your decision. If the pilot does not seem fully aware of the weather risks and ways of mitigating those risks, that would be a bad sign.

You might also want to observe how diligently the preflight inspection of the aircraft is carried out.