On my Polaris Trailboss 250 it starts and idles find but I have to be very slow and gentle with the throttle to get it going. Once moving it accelerates just find until I let it idle down again. Please see the video for a demonstration. What circuit in the carb is likely to cause this?

 

Make sure you have a good fuel flow to the carb.Plus make sure the carb and tank vents lines aren't kinked.If you haven't installed a carb kit I'd do so.Check especially for a wobbly/worn float arm and pin that most people over look and doesn't come with the carb kits. Plus float arm needs to be level with carb body or it can get too much fuel,loading up the crank case with fuel if throttle is applied too quickly.Make sure all jets/passage ways are clean.Normal air/fuel screw setting is 1 1/2 to 2 turns out. Check the air box carb boot for any splits along with the air box neck itself for cracks/splits. They were bad on this type air box about this. Having to slowly give it throttle can either be a rich bog,a sign of too much fuel or it can actually be too lean at higher rpms and can have the same type symptoms.Make sure you have the right main jet. 145 is the standard main jet in most altitudes.If you haven't done a compression check,I'd do so.I've also had some 250 engines idle good enough,but not enough compression to run right off idle and you'd have to go lightly on the throttle as it couldn't take the fuel mixture correctly. Same thing on crank seals,can idle okay,but I've found some that would suck air as rpms increased and cause problems. Usually it's the one behind the drive clutch. Several things to eliminate as the problem as all these things have to work right for the engine to run right. One thing that I can think of that isn't carb/fuel related is to unplug the black wire from the reverse limiter as it can retard timing if it is starting to go out. PLUS one thing after looking at the video again,it looks like it's slow before the clutch engages,like the drive belt is worn or rear clutch ramp button wear,OR it could just be you feathering the throttle slowly taking off..