The Tier extra luggage is only offered on Etihad-operated services + selected partners (Virgin Australia, Air Serbia, ANA on EY codeshare, KE on EY codeshare) if I haven't forgotten any.

You have received the extra Silver allowance from the US as the check-in for the first flight was operated by Etihad so your luggage was tagged all the way with the extra allowance, even if Air Arabia does not recognize the Tier Allowance.
On your way back, as Air Arabia was the first carrier, they do not recognize the Tier allowance and it is not mentioned on the Etihad Guest Partners - even if you are flying on EY codeshare sectors, it was unfortunately correctly denied.
Unsure if that could have been overridden by a Duty Manager.

So, as an example, if I am flying MEL-SYD (VA) - SYD-AUH (EY) - AUH-FCO (EY) - FCO-CDG (AZ) - I'll get my Tier allowance as VA recognizes Etihad Guest benefits.
If I am flying the reverse with the first sector being operated by AZ on an EY codeshare flight, my Tier Allowance will not be recognized as ITA is not a selected Partner that offers the Tier Allowance even if my following sectors allow me to use it.

Frequent Flyers agreements are carriers-specific and adding codeshares into the mix is another level of complexity.
It pays to double-check all details + sometimes pay a bit more to ensure being able to use those benefits for the whole journey.