Lady Arwen is possibly thousands of years old when The Lord of the Rings starts off. But exactly how old was she? What was the age difference between her and Aragorn? Considering the age difference, would not Aragorn seem to be a small kid in front of her?
The Tale of Years (Appendix B) has this entry in the Third Age:
241 Birth of Arwen Undómiel.
So Arwen was 2,777 years old in TA3018 when the War of the Ring happened.
Elrond makes exactly your point when Aragorn first falls in love with her:
"But as for Arwen the Fair, Lady of Imladris and of Lórien, Evenstar of her people, she is of lineage greater than yours, and she has lived in the world already so long that to her you are but as a yearling shoot beside a young birch of many summers. She is too far above you. And so, I think, it may well seem to her."
But she does fall in love with him anyway.
We know this exactly since the appendixes contain birthdates for many characters. Arwen was born in TA (Third Age) 241, Aragorn in TA 2931.
So Arwen was indeed 2680 years older than her husband.
Considering the age difference , would not Aragorn seem to be a small kid in front of her ?
You cannot simply compare age differences the way we humans do among each other. The point is that Aragorn was himself over 80 years old, had travelled extensively across Middle-Earth and survived many adventures, gaining as much experience and wisdom as a human could. Additionally, he was of the royal line of Numenor, so he had some Elven ancestry himself (indeed, Arwen's father is Aragorn's Great-great-<many, many, greats>-Uncle) and inherited some of the innate Elvish nobility along with a greater lifespan.
Even to an immortal Elf who's thousands of years old, someone like that is not in any way a child. Also note that while the Elves themselves take longer than humans to reach maturity (between 50 and 100 years), Aragorn would have been considered a (young) adult by their standards as well.