The system is supposed to work as follows. Butterflies closed, the pump is filled with fuel which has entered from the bleed back valve, now in it's "open" position. If the butterflies are then completely opened, the pump piston will lower itself under its spring tension, overcoming the ball checks and weights, and squirting fuel from the pump jets. Here, I believe, the jet in the side of the exhaust or bleed back jet allows excess fuel in the pump, pushed by the pump spring, to exhaust back into the float bowl rather than continue to be squirted from the pump jets until the pump is empty. The size of the bleed back jet will determine how long the squirts from the pump jets will last. That is, the bleed back jet has two openings. One on top that fills the pump as throttle closes, and one on it's side that bleeds back, or exhausts fuel from the pump chamber back into the bowl, at a metered rate.
So no Eric, you do not misunderstand. I am, after all, the master of the confused and incorrect. If you look at the picture sent earlier, you can understand the multiple function of the bleed back valve, and also why, in racing, it is often a good idea to use a valve with a larger side metered opening, than a (street) smaller numbered jet.
From the picture, you can see only one way for fuel to enter the system, to allow it to drip from the pump jets. Obviously, vacuum will suck more out of these jets, if for some reason, the ball check and weight above is compromised.
As to that compromise, a pressurized float bowl would do it, as will a huge exhaust or bleed back jet, ONLY IF the check valve fails.
Now I get to open a real can-'o-worms. Weber vibration is an evil force. There. I said it. If Webers vibrate correctly, float needles will wear undesirable divots in the float needle rest tab. Float levels can vary, or even stick. It is possible, but impossible for me to prove, that the ball check we just discussed, might leak. Weber conversions lacking outboard front plate support in the form of a PLATE, fastened down low on the block with a rod, will vibrate. Now, more worms. The solid, beautifully machined aluminum connectors that replace the old rubber insulators between Weber and manifold, will only make this worse. The rubber flex was there for a reason, and aluminum insulators or isolators neither insulate or isolate your Weber from the manifold. ANY engine vibration is transmitted to the Weber body, shaking internals at various frequencies. Causing pump jets to drip as check balls and weights rattle around? Maybe, I don't know.
Try this. If your bleed back or exhaust jet is bigger than #80, try 80's. If that does not fix it, and you have checked the ball checks, check the ball check weights. Your 45DCOE14's should be brass. If that does not fix it, and your Webers are correctly mounted, and you do not have the pretty aluminum insulators / isolators, have someone pull up on both Webers while you accelerate, and look in your mirror for dripping. If lifting up on both Webers stops the drip, you have a problem I haven't mentioned.