Don't just ride your bike
Too many cyclists just ride their bikes. Getting to the finish first or producing the quickest time involves many factors not least of which is the condition of your connective tissues,muscles and tendons.
Weight training can improve the strength of the slow twitch muscles allowing them to take on more of the burden of driving the bike forward, thus reducing the role of the fast twitch which can tire quickly. Also as fast twitch muscles produce abundant volumes of lactic, less use of them means less lactic in the blood stream.
Another fear amongst cyclist is that hitting the gym will increase weight, that's very unlikely and although a few athletes maybe predisposed to weight gain the increased power normally offsets the few extras kilos.
And as if you didn't need it another good reason to work some strength training into your program, is to reduce the risk of injury