Even though many weddings are also held at Westminster Abbey (like that of Prince William and Princess Kate), because Princess Eugenie and her husband will be unlikely to inherit the throne, their wedding was more of a personal affair than a state affair with more friends and family in attendance than other world leaders. This makes Windsor Castle more suitable because St. George's chapel is much smaller than Westminster, making it more suitable for this type of event. The community often gets very excited for royal weddings, so having royal weddings at Windsor rather than Westminster makes the weddings feel more personal and like a wedding anyone might have.
Though this tradition isn't connected to the physical environment of the U.K., I definitely believe that this tradition is connected to the overall appreciation for tradition that U.K. society has. In the U.S. we also have an appreciation for history, but our country doesn't have a deeply rooted appreciation for the entire history like people do in the U.K. The royal weddings are an example of that.
