If you don't have the experience to find a prolem on one of the simplest multi venturi carbs ever made (MC) DON't get a Weber! They are a much more complex! (No, I am not hating on Webers... they are fine carbs, but certainly not for the inexperienced)
Give us some more details here... does this only happen at idle? If you give a little gas to increase the rpm and hold it (like, say 1500) will it start to do the same thing there? What motor is this on? What did you take off of? If it's an 87, it probably has the (NASTY) altitude compensator sticking out the back and is actually a 2150, not a much more simplistic 2100.
Rebuild is super simple on these. Instructions available on several sites on the internet. A lot cheaper than buying another carb! Cheap kits available on EBAY.