Mine does have a sort of thumper thunk noise, just like the 650 did, that gets a bit more audible under load. If I lugged down too low it was loudest, kind of like a sign I need to downshift and let it wind up more. In this case I learned rpm can be and is my thumper's best friend. Again after riding last weekend I am learning I am running too low in the rpm too often on dirt/gravel, that I need to let it sing a bit more up around 6000-6500 in general.

 

how old is the gas? did this fuel come from a reputable dealer/station? is it the right rating?

your symptoms... "It is especially bad when moving in low rpms and trying to give more gas".... that sounds like detonation to me, also called pinging, pinking, or spark rattle. old fuel, poor quality fuel, or fuel that is below the required "octane" number (really the performance number) will explode and burn before the ignition sets off the spark. thats the "tink" sound you hear when its happening. it is made worse by guess what...... heat, and load.... "noise only starts after the engine is fully warmed up. It is amplified under load."

it can be very harmful to the engine. I would dump the gas immediately and buy fresh fuel from a know good source

 

fuel grade should be 87, rated by the Ron+Mon/2 method


theres some stuff in the owner's manual about this. if you don't have paper copy, here:
page 38...

file:///C:/Users/a19kl/Downloads/2014-kawasaki-klx250s-52486.pdf

anyway, thats where I would start

 

at first I thought spark knock as well, drained fuel tank filled back up with premium 92 octane and dumped a little sea foam in there. still there after three refills, I drilled the welch plug out for the fuel screw and gave it 2 turns out from seated and it seemed to help. engine runs smoother and a more constant rpm rather than jumping around and trying to die when not completely warmed up. now on deceleration I'm getting backfires, gentle popping in the muffler. this thing is completely stock, so I'm wondering if I should put a jet kit in it of some sort and a good cleaning. may be a slip on muffler of some sort.

any suggestions on which way to go?

 

Gentle backfire it pURRRFECT!