recently installed 650cc, ~300 miles in. Starts and runs great.
Has begun to hesitate on acceleration. ASSuming it's a fuel issue.
Fuel Filters? Carb? Jets? Air filter? valve adjustment?
here is video of what is sounds like
https://youtu.be/5RFJkha60oU
If the engine didn't hesitate on acceleration initially but now it does, then something has changed. 300 miles isn't much so I'd check valve clearances, idle jet (accessible on the side of the carb - so no need to strip it) and ignition timing. If everything checks out ok, I'd try advancing the ignition timing a little just to see if it helps. I worked in a Fiat dealership back in the day and sometimes had to do this to cure a problem child - as long as the engine doesn't 'ping' when accelerating in top gear, it shouldn't do any harm. (ymmv)
As 'The Whitakers' has (have?) said, the lack of an accelerator pump in the carb tends to result in the type of hesitation you describe, occurring just above idle, and not present if idle speed is raised significantly.
However, single choke Weber fixed-choke carbs have what is called a progression circuit. When the throttle valve is opened slightly from the idle position, there is a tendency for the mixture to lean-out and thus cause the engine to hesitate/bog down. To overcome this problem, one or more transition orifices (aka progression holes) are drilled in the inner wall of the carb barrel, intersecting with the idle fuel circuit, just above the edge of the throttle valve (aka butterfly valve). As the throttle valve is opened from the idle position, these holes are now subjected to engine vacuum and allow some extra fuel to flow from the idle circuit, hopefully

preventing the mixture from going too weak and thus avoiding hesitation. As the throttle is opened further, fuel is supplied from the emulsion tube/main jet and finally from the main jet.
These progression holes don't pass any fuel at idle speed as the throttle valve is almost closed, thus they don't experience any engine vacuum. Also, both the idle jet/hole and progression holes don't pass any fuel when the throttle is more than say 1/4 open as they are no longer experiencing enough vacuum to cause fuel to flow, the engine is now running on fuel supplied by the emulsion tube and main jet.
The reason the engine doesn't hesitate when the idle speed is raised to e.g. 1200 rpm is that the progression holes are now in action.
On the larger twin-choke 'sporty' Weber carbs, there can be up to 5? staggered progression holes in each carb barrel. Sometimes there's a removeable plug, so you can drill more/mess with things/mess things up and then re-seal with another plug.
On less 'sporty' carbs, you might befriend a Dentist, these guys have brilliant little high speed right angle rotary burrs which are ideal for drilling/enlarging progression holes. Another option is to modify i.e chamfer or notch, the edge of the throttle plate (butterfly valve) so that the progression hole/holes are uncovered a little earlier and subjected to engine vacuum so that they flow fuel a little earlier.
Just bear in mind that while it's easy to drill holes, it's not so easy to undrill them.
Any time I hear of someone having carb problems and they mention that they previously fitted a new butterfly valve and spindle, I can't help but wonder if they got the new valve exactly centralised - it doesn't take much misalignment to really mess things up.
I vaguely seem to recall that one of the 500's or 126's was fitted with a carb that had an accelerator pump? Hopefully, the cognoscenti will chime in to confirm or refute.....
Al.