The float valve is not a fuel shut of device. If it where then they wouldn't put a petcock on there. The float and valve are a metering device. It is designed to keep the fuel in the float bowl at a certain level while the bike is running.
If the pet cock leaks the weight of fuel in the tank can cause fuel the leak past the float valve. If your bike sets in the sun the heat build up can cause fuel to leak past the float valve.
Any moisture that collects in the bottom of the tank gets into the petcock and can corrode the aluminum parts. There is a rubber disc inside. This disc has holes in it that are opened and closed as you turn the petcock on/off. The lever you turn has a flat disc that sets against the rubber disc. The flat part has a groove in it that connects the holes in the disc to control fuel flow.
If corrosion builds up on the flat part that sets against the disc it can rough up the rubber enough that it won't seal well. This is where the fuel you get on your fingers comes from.
To fix you remove your pet cock, tear it apart polish the flat surface with 400 grit or finer sandpaper till smooth, bright and shiny. Put the sand paper on something flat and be careful to keep the flat surface of the petcock part flat.
I had the same problem on my 75.
Also remember to shut the petcock off everytime you turn the bike off. This will prevent fuel leaks at the carb while not riding the bike.
Because you have the fuel running out the over flow your float valve in the carbs are not sealing. It is probably dirty float valves, or mis adjuste or leaking floats. Need the remove, clean, inspect the carbs.
www.amckayltd.com/carbguide.pdf will help with that.
Leo