Sounds like running rich. Possible causes: misadjusted float in the weber, or leaking float needle valve, letting fuel leak into the carb throat. Or, if the carb was installed without a fuel return line and pressure regulator between pump and carb, the pump may be overwhelming the needle valve, and flooding the carb that way.

Effects: combustion chambers get carboned up, and some of the deposits glow white hot, hot enough to ignite fuel without a spark, which is all you cut off with the ignition switch, so it "diesels" on. Backfire on closing throttle at speed with a leaky carb is the excess fuel igniting in the exhaust pipes/manifold/cat/muffler.

How is your fuel mileage? How does it run otherwise? Any smoke from exhaust at idle, and does it smell like gas? Don't huff too much, or you'll die...

Could also be grossly wrong timing. Any pinging on accel? Is accel more sluggish than normal?