The earth's rotation at the latitude of Florida and California is approximately 30°, That gives us a velocity of 0.40 km/sec or approx. 900 miles per hour. Back before I went to medical school I did the exact calculations, but here goes the quick approximations.

Orbital velocity at Earths surface is 7.91 km/sec
Shooting the rocket from west to east, we need to increase speed by 7.51 km/sec.
Shooting the rocket from east to west, we need to increase speed by 8.31 km/sec.

The need for more speed will require more propellant, and reduce the amount of payload.
Tsiolkovsky rocket equation: Change in Velocity = Ve* ln (Total Mass / Payload Mass)

*Assuming perfect conditions and avoid structure weight and other assumptions*
A single stage rocket with a 4.5 km/sec exhaust speed requires
West to East ---- u=1–1/exp(7.51/4.5)=0.811 (18.8% of weight is payload)
East to West ---- u=1–1/exp(8.31/4.5)=0.842 (15.8% of weight is payload)


You end up getting about 30% more payload weight by launching West to east, which is awesome considering how expensive space travel is.