In a sincere and heartfelt manner:
— I would dearly love to know.

synonym: in a heartfelt way.

At a great cost:
— He paid dearly for the food.

synonym: dear.

Roget 814: dear, dearly; at great cost, heavy cost; a grands frais [Fr.].   

With affection:
— She loved him dearly.

synonyms: affectionately, dear.