Here is another way to look at this problem. When you stand on a scale, the force the scale experiences is equal in magnitude to your weight. What we normally sense as weight is the reaction of the surface on which we stand. The scale is calibrated to read mass and thus actually reads N /g.
Since you re spinning along with the earth, circular motion comes into play, and we need to consider the centripetal force which is the resultant of mg acting towards the centre of the earth and the normal reaction say N acting outwards ( note m here is your actual mass.) Thus ( mv^2 ) / r = mg  N, which gives us N = mg  ( mv^2 ) / r . Dividing throughout by g, we get N/g = m  v^2 / rg. Since N/g is what the scale reads, as your mass, your actual mass m = N/g + v^2 / rg and is thus greater.
And "a buoyancy force equal to the volume of your body under water times the density of water" that should be the weight of the volume of water displaced, so it needs to be multiplied by g
