How do you know it is over fueling?
Over fueling as in running rich? At idle, when running at some off idle TP? Cold, hot? Do the fans come on at key on engine not running?

Rich Immediately at start should eliminate the O2 sensor as it is not in closed loop at that point. A GS911 or a trip to the dealer might uncover a faulty component like the engine temp sensor. If the fans are on at key on, it is the temp sensor open circuit. Check to make sure the plug is secure, bottom square one on the left side of the battery under the tup. If secure and fans don't come on with key, you can check it with a meter based on the engine temp or if cold ( better) , ambient temp by this chart measured in ohms. If it is close, then possibly a leaking injector only discoverable by visual inspection pulling the fuel rail and letting the pump pressurize and looking for leaks. Vacuum leaks will cause it to idle poorly, usually high.

---------------------------------------------------------
TEMP (in celcius) -vs- resistance (Ohms) for various cases:
---------------------------------------------------------
8 .......... 4000
10 .......... 3880
14 .......... 3290
20 .......... 2570
25 .......... 2130
30 .......... 1760
35 .......... 1462
45 .......... 1049
55 .......... 727
65 .......... 540
75 .......... 392
85 ..(thermostat opens).. 296
95 .......... 229
105 ..(fans activated temp).. 187

---------------------------------------------------------
TEMP (in Farenheit) -vs- resistance (Ohms) for various cases:
---------------------------------------------------------
46.4 .......... 4000
50 .......... 3880
57.2 .......... 3290
68 .......... 2570
77 .......... 2130
86 .......... 1760
95 .......... 1462
113 .......... 1049
131 .......... 727
149 .......... 540
167 .......... 392
185 ..(thermostat opens).. 296
203 .......... 229
221 ..(fans activated temp).. 187

 

May be something in the mass air flow sensor is a bit off. I don't believe that bike has a O2 sensor...

 

Patric is correct. No O2 sensor so it would have to be a dirty Mass Air Flow sensor. Search the web for ways to clean it as it is a $956 (ouch) part.

 

My bad on the k100 as I was thinking K1100. Didn't know it used a MAF and $956 to boot. Double ouch.

 

If your symptoms are 25mpg and a strong smell of fuel from the exhaust....this happened to a friends K100.
IIRC.......It was a valve in the injection system, instead of returning unused fuel to the tank, it was pushing the extra fuel into the cylinders, thus poor mpg and smell of fuel.
I don't think the fix was either expensive or difficult.

Sorry I can't be more specific on which valve.....it was a long time ago and there are dozens of real ale breweries around these parts>