No in-line filter? That's a good place to start. You didn't tell us if this is a Chinese 2 stroke kit but if so the fuel tanks that come with them are notorious for containing rust, dirt and crud that should have been flushed out before you installed the tank. Even with a clean tank a fuel filter installed between the tank and carburetor is a good idea.
The smallest dirt particle can block the float needle valve from closing and will allow fuel to gravity flow from the tank and leak from the carb.
Clean your carburetor, flush and clean the tank then install a filter. I think that will cure your problem. But, when the bike is parked the fuel petcock should be turned off. That's why a petcock is provided with the kits and why most motorcycles have them.
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