When they say they love each other, they mean it sincerely.
Advanced English Dictionary
+adverb in a way that shows what you really feel or think about sb/sth: I sincerely believe that this is the right decision. + 'I won't let you down.' 'I sincerely hope not.' Idioms: Yours sincerely (BrE) (AmE Sincerely (yours)) (formal, written) used at the end of a formal letter before you sign your name, when you have addressed sb by their name
Random quote: True happiness means forging a strong spirit that is undefeated, no matter how trying our circumstances.: Daisaku Ikeda