That's what I suspected.
It's it likely a combination of dried out seals and gunk clogging up the floats.
Order a set of gaskets (don't waste time and money on kits that include needles and jets). Pull the carbs (heat is your friend, use a hair dryer to warm the insulators that connect the carbs to the manifolds). Buy a couple cans of carb cleaner, visit the local guitar shop for a few scrap pieces of E string, and give the carbs a good cleaning.
It's not a hard job and you should be able to do it in a single weekend, but plan to use every bit of the two days. It's not a job that can be done in 2 or 3 hours, especially if you are learning as you go.