Growing up, Grandpa Portman was the most fascinating person I knew. (Prologue.2)
Ignore the misplaced modifier here. Jacob is talking about how when he was growing up, Grandpa Portman was fascinating. Or maybe he means that Grandpa Portman was fascinating when he was growing up, too.
When I was six I decided that my only chance of having a life half as exciting as Grandpa Portman's was to become an explorer. (Prologue.3)
They say that imitation is the sincerest form of flattery. Young Jacob wants to pretty much be his grandpa, so he tries to imitate his adventurous ways.
I realized it wasn't just my grandfather's life that Miss Peregrine had saved, but mine, too, and my father's. (3.42)
Jacob has a sort of built-in respect for Miss Peregrine. He recognizes that if she hadn't taken Grandpa in, well, none of his descendants would have ever been born—Jacob included.
Jacob Magellan Portman
"It's amazing, isn't it? Everything he went through." (4.127)
Jacob tries to see the good in Grandpa, though, and tries to understand and admire his accomplishments, like the fact that he survived the war and always lived with honor.
It was true, of course, what my dad said: I did worship my grandfather. (4.52)
Jacob's dad thinks Jacob's admiration of Grandpa Abe is unhealthy because Dad doesn't think that Abe was a good person. To Dad, Grandpa is hardly a role model. He's just an adulterer and a bad father.
"This is Abraham's grandson, Jacob. He is our honored guest and has come a very long way to be here. I hope you will treat him accordingly." (6.149)
It is clear that Miss Peregrine and the rest of the children in the home respected Jacob's grandfather very much from the way they treat his grandson.
I was duly impressed, and told him so. "I'm glad someone appreciates my work," [Millard] replied. (7.88)
The other kids don't appreciate Millard's cataloging of the day-to-day events of Cairnholm because they live them everyday. Since Jacob is an outsider, though, he thinks it's pretty cool stuff.
"I know he would've been proud of you," [Emma] said. (10.338)
This is nice of Emma to say. She knows that Jacob would have done anything for his grandfather's admiration while Grandpa was still alive, so she gives him a little taste of it.
He was one of the most honorable men I have ever known. (11.147)
This is perhaps the most important thing Emma can say in her letter to Jacob's dad. Maybe it will let Dad finally see what a good man his own father was, and give him what he needs to become a good man himself.
I told [Emma] I was [staying]. Tired as they were, the children whistled and clapped. Some embraced me. Even Enoch shook my hand. (11.64)
By the end of the book, after Jacob has rescued Miss Peregrine, he gets the kind of admiration from the other kids that his grandfather should have received in life.