I assume because of Aria's behavior, she might have dirt on Tavos. So maybe lewd or taboo or something else to blackmail. It is hard to tell if by writing or by purpose when the councilor just quickly sides with Aria. Could be loyalty of friendship, or because she know Aria has some DEEP evidence of something Tevos doesn't want to be revealed. I go with the latter because Aria doesn't strike me as friendly or honest with everyone she knows.
Maybe and I am making up an iceberg here...
Aria did help Tevos maybe in some manner, and the Asari at most times than try to openly show themselves as high up. Perfect, civilized, and classy people. Thessia is nice looking(before Reapers).
Especially since we find out the Asari witheld a lot of Protheon knowledge(Not saying Aria knew about that). But like I said it could be just related to Tavos having some maybe in blackmail. Like having evidence of Tavos's "questionable" Matron days. I remember some Asari in the second or first game said soemthing about a lot of Asari furing matron years is bassically that party years of there life.
It would be like if the representative of the U.N for the U.S was involved in human trafficking. It will not look good tobthe other countries ans brings up questions about the integrity of the country beinf represented and people. Whether or not anyone can do anything about is besides the point. But the U.S government will be under heavy strutiny for suspect of someone in such a position of power being involved in human trafficking. Or even now. Being suspect of doing or have done drugscan be bad for any politician.