I've found (going from a less powerful bike) theres a few issues that have been causing me to run wide alot too:
Its alot more powerful, and if I don't commit to the corners (leaning far enough and with enough speed) then I often go wide.
The rear brake lever is too high for me and changing it makes it way too low, so I can't put my weight into that peg for turning (putting the weight into the pegs when turning makes the bike feel totally different, and respond really well)
First gear is good till well past 40km/h but trying to corner in it it just seems to have too much torque, generally much better to stay in second, I'm not technical, but in first accelerating through corners the bike wants to stand right up, or the power through the back wheel makes it skip out
I'm about 70kg, in gear so it might be those factors. Generally knowing what gear to be in and having confidence helps a huge amount however, hope thats helpful, otherwise check your suspension to make sure the seals haven't gone if its an old bike.
I won't try and advice on changing the suspension because its different than on my old bike, BUT it might be as simple as pulling a thin metal bar into the slot and either pushing it up or down a notch. Would need to take a look and its probably worth getting someone with more experiences help.