The weather information is provided through MSNBC. The weather shown is for the nearest weather observation station available through MSNBC. Some will provide you with accurate weather information on the highpoint itself. Others will vary greatly from the actual weather conditions on the highpoint. Whereas the weather link on Ebright Azimuth (Wilmington, Delaware weather) will be very close to the actual weather at the highpoint, or in the case of Mount Washington, (where there is a weather station located on the highpoint) the weather will be right on point, some highpoint weather information provides weather for locations well below the summit.
Weather conditions vary greatly on some of the taller highpoints, and the information provided through the weather links is listed as a starting point. If you plan to attempt a climb on any of the taller or more challenging highpoints, be prepared for any type of weather conditions.
Here's the weather link for my home town: