It's the other way round! An aircraft's apparent weight (mass always remain's the same) is less when travelling east. The effect is maximum when heading 090°T at the equator. (That's why space vehicle launch sites are close to the equator and they launch heading in an easterly direction!) Anyway for an aircraft travelling east at the equator at 500 KTAS the apparent weight reduction is about 0.9% At a speed of 1200 KTAS (Concorde) the weight reduction is 1.9%.
If you want a longer technical answer (High School Physics type equations) then e-mail me.