'support the theory' is correct and usable in written English.
For example: The data collected in the experiment strongly supported the theory.
"You amass evidence to support the theory".
There is plenty of research to support the theory.
Unfortunately, there is little evidence to support the theory.
Observations of the solar system itself support the theory too.
The experimentally obtained results support the theory surprisingly well.
The official acknowledged that there was still no hard evidence to support the theory.
The people can't absorb and support the theory of an Islamic state.
"There's no real evidence to support the theory Omar threw a hand grenade," Commander Kuebler said.
But virtually all scientific experts support the theory that greenhouse gas emissions contribute to warming.
The scene seemed to support the theory that Mr. Dudamel can resist Important Maestro Syndrome.
There were no WMDs and little intelligence to support the theory that they existed.
