Come on gents...
Washers or not...fuel flows from the bowl...thru the petcock..down the fuel lines or line.
I have had a very similiar problem many times.
Heres what the culprit has been in my case's.
1. Corrosion of the mating surfaces in the petcock. Sometimes the lever arm itself has been pitted severely. Enough to allow fuel to seep past.
Sometimes the surface inside the petcock body itself has been corroded...same result. Large pits and then the rubber washer doesn't seal.
2. Damaged holes in the body. Sometimes they are corrosion damaged causing the small lip to chip off.
Below is some of the corrosion damage I'm talking about....
Note the corrosion damage to the lever.
Note the corrosion damage to the bowl mating surface..