His social position is ambiguous at best. Amelia and Gideon grew up together as best of friends. And now, Gideon feels compelled to protect her from her cousin and from all the other fortune hunters who might threaten her. He owes it to his benefactor. A duke's daughter cannot marry a nameless foundling, however much he has made of himself.
Amelia has no plans to marry anyone.
She intends to devote her life to the charitable works that she shared with her father. If she has an unspoken tendre towards Gideon, she is unsure how he feels about her. It well could be that he simply loves her as a sister. Of course, Eustace becomes more and more desperate, especially after Amelia roundly rejects his proposal. Pressured by his ruthless creditors, he agrees to a plan to abduct his cousin.