Here's how it breaks down:
* Very: Emphasizes the sincerity and genuineness of the sentiment.
* Truly: Indicates honesty and authenticity in the writer's feelings.
* Yours: Shows a sense of belonging and connection to the recipient.
While still common, "Very truly yours" is considered a more old-fashioned closing and is becoming less common in modern correspondence. It is best suited for formal occasions or when addressing someone you have a more formal relationship with.