Would the centrifugal effect of the Earth orbiting around the sun cause the weight of an object to change? If you weighed an object at mid day and then again at midnight, would the objects weight change ( ever so slightly ) due to the centrifugal effect of the earth travelling around the sun ?
What I am trying to understand is if the object is weighed at mid-day the centrifugal effect however slight would press the object against the scales - where as 12 hours later when the same object is on the far side of the earth the centrifugal effect would do the opposite and marginally push the object away from the scales causing it to weigh a little less ?
 A: No, there is no effect of the type you're imagining. The earth is free-falling through the gravitational fields of the sun and the moon, and therefore we experience apparent weightlessness with respect to our weight in those fields. This is similar to the apparent weightlessness of astronauts aboard the ISS. Just as those astronauts can't tell by any experiment, without looking outside, the difference between up and down in the earth's gravitational field, neither can people on earth tell by gravitational experiments the difference between the sunward and anti-sunward directions. Apparent weightlessness occurs because you and the object you're using for reference (earth or ISS) are free-falling together, with the same acceleration.
Cf. Weightlessness for astronauts
We can detect the (fictitious) centrifugal force of the earth's rotation, but this is constant in time, so it just causes a variation of the earth's gravitational field (measured relative to the earth's surface) with latitude.
The only time variation is due to tidal effects. These have a period of 12 hours (not the 24 hours you were imagining), and are quite small. Tidal effects slightly decrease your weight when the moon or sun is overhead and underfoot. They arise because you and the earth are at different distances from the moon or sun, so you accelerate slightly differently.  The lunar effect is about $10^{-3}$ m/s2, which is about the same as the effect due to changing your elevation by 30 cm.
