My weight = 65kg (let's suppose it's my mass m). Actually weight is not mass. Weight is force (my mass will be the same, but my weight will change). Weight is a force F(w)
To calculate v, we suppose I'm at the equator: r = 6.378.000 m (diameter is not 8000km Kraw)
With 1 period = 8h = 28800 sec, v = Pi*2*r/28800sec = 40074249 m/28800sec = 1391 m/sec
So F centrifugal = 65 * 1391² / 6378000 = 19 Newton (direction is off cource away from earth).
Do the same with the 'normal values', you get the current F centrifugal = 2 Newton. Thats a difference of 17 Newton.
So my "weight" would be reduced by 17 Newton
Here you go