In most cases, weather will not affect your flight, except for the occasional bump. Your air charter flight can not depart when the weather forecast indicate a safe flight can not be completed or if the weather at the destination airport is below minimums as describe below.
If the weather at your destination airport goes below the set landing minimums, your pilot will have to land at an alternate airport, and the difference in flight time may be added to your cost of your air charter.
In Air Denver's 30 years of operation, we have seen very few air charters not be completed because of weather. The regulation that requires a plane to stay on the ground if the flight can not be completed in the forecast weather is a good one. If your flight is cancelled due to weather, there is almost always no cancellation penalty.