'becomes thinner' is correct and usable in written English.
You can use it to describe something that has been reduced in size or width. For example: "As the ice slowly melts, the lake becomes thinner."
Reality becomes thinner and finally seems to tear away altogether.
Toward the tail the body becomes thinner and yellowish red.
As we get older, our hair becomes thinner and more limp.
As users get faster, the test gets harder: the frame around the bottles becomes thinner.
As a result, the cartilage, becomes thinner, and the long bone.
This strong muscle wall expands and becomes thinner as a child develops inside the uterus.
Many women notice that their hair becomes thinner and drier and their nails more brittle.
At higher altitudes, the air becomes thinner and the amount of breathable oxygen decreases.
The jet elongates and becomes thinner, and dries into a nanofiber.
Without radiation, the reaction zone becomes thinner and the ignition is delayed.
This region becomes thinner as the frequency of oscillations is increased.
