"To support the thesis" means to provide evidence, reasoning, or arguments that strengthen or prove the main idea or argument being discussed or presented. Full definition
You should identify points that support the thesis statement of your essay. (essayacademia.com)
And climate research scientists are fully aware that it is difficult to publish results that do not support the thesis of disastrous AGW. (judithcurry.com)
The contributors avoid evidence that does not support their thesis that feminism is dangerous to the church. (religion-online.org)