"Flimsy evidence" refers to evidence that is weak, lacking in substance, or not convincing enough to support a conclusion or belief. It implies that the evidence is not solid or reliable. Full definition
There were also civilian detentions in military facilities, often based on flimsy evidence; denial of fair public trial; executive influence on the judiciary; infringement on citizens» privacy rights; restrictions on freedoms of speech, press, assembly, and movement (nigeriapoliticsonline.com)
A tribunal found that the Home Office has deported thousands of students from Britain based on extremely flimsy evidence. (politics.co.uk)
And — on such flimsy evidence, why do you believe it at all? (judithcurry.com)