+1 on what Laitch has said. When was the last time the bike was serviced(oil change, plugs, filters, etc.). Besides fuel, which is the first thing I would consider, how old are your spark plugs? I ask because opening the throttle under load will increase the compression pressure in the cylinder. An old plug will have trouble firing under pressure where it will fire fine at idle or in neutral.
If you can't remember when the plugs were new, spend a few bucks and replace them. If you get NGK D7EA plugs, get some terminal nuts for the top. You need them to get a reliable connection from the BMW plug wire. If you don't have any nuts, you can usually get three of them at almost any repair shop, especially one that works on small engines(lawnmowers).
While you're at the auto parts store, get a new fuel filter. The NAPA gold 3032 is a very good one.
Then remove the filler cap, and before you replace the filter run the engine and watch to see if there is fuel spraying out of any of the connections. Some dripping from the roof of the tank is okay, it's just the fuel returning from the regulator. Is the inside of the tank nice and clean? Is there a bunch of black goo all over the place?
After you check the connections install the new fuel filter. Don't use the fuel line that comes with the new filter, it's not rated for use in the tank and will dissolve. Use the old stuff and make sure the clamps are snug. Then run the engine again and check for fuel line leaks before you replace the filler cap.
When you've done that stuff, get back and let us know if things are still not right.