... canecorso, the stock Triumph seat (driver's seat only, no passenger seat involved) weighs 6 1/2 pounds. Measurements of seat are: 19 3/8 inch long, 16 1/4 inch wide and 5 1/8 inch tall / thick. I have pictures but don't know how to post them here for you yet, but I am trying!
I had the same problem on my 1994 Sprint which had the same basic motor. I took the petcock apart and found that the vacuum orifice is tiny, barely get the tip of a needle through it and it was blocked with dirt. This caused the thing to stay open and leaked gas. No idea if it is the same problem but I would have a look inside first. Easy job.