The group hug at the end of 5x06 was so much more powerful than Ruby hugging Weiss ever could have been. Weiss standing there all alone and crying while she lets the sisters have their moment together is incredibly heartbreaking, especially if you remember that Weiss doesn’t have any family left apart from Winter and Klein who are both in Atlas right now.
Of course Ruby would hug Yang first. But then they notice Weiss. They see her and Ruby calls her name to pull her out of her lonelyness. And Ruby does not only go and hug Weiss, she and Yang open up their very peronal and private family moment for her. They don’t just include her into this hug, they also include her into this family. It’s such a strong symbolic moment and it acknowledges her and their bond more than any individual hug ever could. And Weiss is so so happy when they do it.