Why does the word "forever" seem to strike the stranger as interesting?

At the beginning of chapter 4, Winnie is outside playing in the yard. The man in the yellow suit comes by and begins asking Winnie about her family and how long they have lived in the area. Winnie answers by saying that her family has lived there "forever."

"Perhaps. In a bit," said the man. "But I'd like to talk to you first. Have you and your family lived here long?"
"Oh, yes," said Winnie. "We've lived here forever."
"Forever," the man echoed thoughtfully.

What Winnie means is that she has lived there a long time, but it peaks the man's interest because he is hunting for a family that supposedly lives forever. He explains in chapter 19 how he came to learn about the improbable family.

"As I've told you, I was fascinated by my grandmother's stories. People who never grew older! It was fantastic. It took possession of me. I decided to devote my life to finding out if it could be true, and if so, how and why."

For twenty years, the man in the yellow suit tried to learn more about the immortal family, but he always came up with nothing. After encountering the Tuck family, the man in the yellow suit explained how he finally decided to try and retrace the Tucks' path. The man in the yellow suit is obsessed with the Tuck family because he wants to figure out how they became immortal. With that knowledge, his plan is to sell the immortality-bestowing spring water for profit.

"I'm going to sell the water, you see."
"You can't do that!" roared Tuck. "You got to be out of your mind!"
The man in the yellow suit frowned. "But I'm not going to sell it to just anybody," he protested. "Only to certain people, people who deserve it. And it will be very, very expensive. But who wouldn't give a fortune to live forever?"

That's why the man in the yellow suit is so interested in the word "forever." It's another clue that will get him closer to his get-rich scheme.