Assuming you have checked for a good fat spark when you put the plug in and that side of things (plug, lead and earthing is all good 
Whats the plug like wet?? or dry.
If its lean check your Carb to engine boot for cracks
If its wet it'd have to be wet not just black for this condition imho?
Check the Choke Circuit is shutting off.
Check the breather tubes out the carbs we had something similar when we didnt let enough air into our dump bottles (holes to tight) carb is pressuring.
Had the same on a CR250 I bought it as a bike that was having trouble. They'd run it through the mud and the dump tubes were caked with mud up inside blocking them. Cheap Bike that was 
Secondly make sure the float valve is seating and not letting to much fuel in.
Rudimentary test is: Turn the carb upside down and gently blow through the inlet the weight of the floats should seal the needle valve.
Check the float levels.
Then its jetting.
Check for spec's on needle etc but it should rev to 1/2 throttle ish without even a main jet installed.
Dont just give it a fistful you have to check the progression
Ie Pilot jet just cracked, Mid+Needle and emulsion tube there to 1/2 and from there main on up to full throttle.
Remember the Pilot lets fuel in off throttle as well is it bogging after the second or third twist?
Main rule you cant blow a 2 stroke by going rich, you can by going lean.
My guess if its truly fuel bogging its your float level, Needle valve or reeds are not sealing?
Research Std specs for, Pilot needles etc Std specs are a damn good pace to start on a bike that could have been fucked with since 2002.
My 2c all care no responsibility LMAO :P
On a Motorcycle you're penetrating distance, right along with the machine!! In a car you're just a spectator, the windshields like a TV!!
'Life's Journey is not to arrive at the grave safely in a well preserved body, but rather to skid in sideways, totally worn out! Shouting, ' Holy sh!t... What a Ride!! '
Bookmarks