Fuel is gravity fed, no pressure. Is the drip coming through the hose, or out the screw you have circled? That’s the floatbowl drain screw, make sure it is snug. The tube also leads from a long pipe inside the bowl that is the overflow of the float needle is sticking and letting too much fuel in the bowl. Try tapping the float bowl with a metal tool (I usually use the handle end of a 3/8” ratchet handle). If that doesn’t do it, pull off the floatbowl. Often the floats are stuck in dried up fuel in the bottom of the bowl.
Alternatively, it is not uncommon for the over flow tube (inside the floatbowl) to have a small split in the brass, near the bottom. I believe moisture accumulates there, in a dry carb, and then freezes and splits the delicate fitting.......
Don’t be afraid to pull those float bowls. There will be lots of dry fuel crud in there. You don’t want to soften it with fresh fuel and then plug your idle and main jets.....