That tube is probably the overflow - it's there to keep the carb from completely filling up and flooding your air filter etc with fuel.
Your problem is probably with the float valve.
There is a float inside the carb and when the fuel bowl on the bottom of the carb fills up, the float rises and puts a small "needle" into a hole to stop the fuel from coming in. But if a tiny piece of crud blocks the needle, or the float gets stuck down, or the float springs a leak and stops floating, gas just keeps on coming in and it has to go somewhere - so it overflows.
I had some of that on my Ranger when I got it. The carb was all gunked up from sitting. I had to take it apart and clean it - twice - before the machine would run properly.
Bottom line, you probably need to go into the carb and clean it up real good.