Romanian term (edited): fără însă a se absolutiza vreunul

If it really says fata, then it's a typo. It should say fără.

This phrase is about the weight, or importance, that is attached to the various factors when making a decision. They are criteria that a court considers when deciding what is in a child's best interests, especially when deciding who will look after the child.

The point being made here is that no single factor is decisive all on its own or outweighs the others in all cases. The court will base its decision on a combination of these factors considered together in the particular circumstances of the case, and will decide how much weight to attach to each factor according to the circumstances.

If we look at the same phrase in this similar sentence, there is a clue at the end, which I have underlined:

A aratat instanta de recurs ca in doctrina si practica judiciara s-au consolidat acesti factori: posibilitatile de dezvoltare fizica, morala si intelectuala pe care copilul le poate gasi la unul dintre parinti, legaturile afective stabilite intre copil si unul dintre parinti; comportarea parintilor fata de copil; posibilitatile materiale ale parintilor, varsta copilului si starea sanatatii acestuia, serviciul si moralitatea parintilor, iar pentru a fi respectat principiul interesului superior al copilului, acesti factori trebuie analizati in stransa concordanta cu starea de fapt existenta in speta, fara a se absolutiza vreunul dintre acesti factori in detrimentul celorlalti...
https://www.avocatura.com/speta-44678-minori-si-familie--sta...

So here, no single factor is treated as being of paramount importance to the detriment of all others. In other words, it is not given overarching/overriding importance.