"empirical support" is a correct and usable phrase in written English. You can use it to describe an evidence-based argument or conclusion. For example, "The study offered empirical support for the hypothesis that early childhood education is beneficial for cognitive development.".
There is some empirical support here.
Bluntly, there is little empirical support for this hypothesis.
There is some empirical support for this hypothesis.
Yet the empirical support for this is weak.
The empirical support stemmed mainly from historical evidence on lynchings of blacks in the South.
Most of the hundreds of psychotherapies have no credible empirical support for their effectiveness.
In recent years, there's been some empirical support for mild versions of the Whorfian idea.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union