I did some weight work on the legs years ago. It never seemed to help my cycling a lick.
But weight work is usually based on working until muscle fatigue. If you do that, you really should take the next day off or do a really moderate recovery ride.
I think, as others have suggested, this might work best for the winter season. It is summer and prime bike time. If you want to work on strength, you can do sprints, intervals or climb steep hills.