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if I slooooowly open the throttle it hesitates a bit. I'm thinking of removing the weight in the AP circuit, as some people have gotten an improvement after doing that?

Removing the weight might fine tune it a bit but there's a major problem there besides the weight being there or not being there. You should have a squirt immediately whether you open the throttle fast or slow. I'd open her up again maybe check the condition of the neoprene AP cup & if good there then why is it not building pressure or where is the pressure going instead of out the nozzle?. A good visual inspection inside there is in order.

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