Which Askr Trio weapon to refine

Probably Sharena. Warping with Anna is worthless in terms of combat utility and Triangle Adept makes it near impossible for Alfonse to get counter triangle kills, which will hurt your arena score if you use him as a bonus unit.

Alfonse, he benefits incredibly well from them. He gains a built in brazen from his weapon from refining it. Stat boosts are the way to go if you’re gonna refine him. Defense is the best stat boost out of the 4. If you do refine it with defense, you should probably give him bonfire as well.

Res or Def Refine on Alfonse works great and the effect Shareena's is also pretty solid. As for Anna... just give her a Slaying Hammer+.

I already refined Sharena weapon. And my next refinement will be Alfonse one since I got Brazen DEF/ATA (A slot) for him. He will become a phisical monster when he is lower than 80% hp. A +def refinement will be perfect for him.

Unfortunately, Anna's isn't that good, so that's a low priority unless you really like her.
Sharena's is fantastic as she is already a nice duelist pre-refine. But of the Askrtrio, Sharena is the best on her own and very flexible, and therefore she isn't in dire need of her refine.
Alfonse could stand to use his refine the most. Especially with the sheer number of swordies diluting the pool, he's not all too special on his own. His refine, however, is fantastic and provides him with the broken Brazen effect. It's perfect for him. And you are making a good choice ignoring his effect refine. Compared to such a nice base effect, his "special" refine just sucks, and is only useful if you want to want him as a specialized Green killer, but at that point, you're better off using Hinata, if only to save your Divine Dew and use it for an actually good refine.