Skull liked Tsuna, had been drawn in by him, but it is not until he hears Tsunayoshi Sawada declare that he would destroy Vongola before he would inherit their sins that he respects him.

Skull had never mentioned it, but he had been loyal to Giotto all those years ago. He hadn't been his Guardian, but he had been an advisor and had protected him a few times when his Guardians had been otherwise occupied. (A bit like Reborn is to Tsuna actually)

He would have stayed loyal to Vongola if they had stayed loyal to Giotto's ideals when he moved to Japan.

They hadn't- they had walked down a path bathed in blood- and so Skull had moved on though he kept an eye on each generation after just in case.

When Tsunayoshi comes along and he tells the world that he will burn Vongola to the ground before he takes on their sins, and Skull can see he means it

Skull grins.

This would be Giotto's true heir.