Should

What do 'would' and 'should' mean here?

A few minutes after Angela left with the hikers, Jacob sauntered over to take her place by my side. He looked fourteen, maybe fifteen, and had long, glossy black hair pulled back with a rubber band at the nape of his neck. His skin was beautiful, silky and russet-colored; his eyes were dark, set deep above the high planes of his cheekbones. He still had just a hint of childish roundness left around his chin. Altogether, a very pretty face. However, my positive opinion of his looks was damaged by the first words out of his mouth.

"You're Isabella Swan, aren't you?" It was like the first day of school all over again.

"Bella," I sighed.

"I'm Jacob Black." He held his hand out in a friendly gesture. "You bought my dad's truck."

"Oh," I said, relieved, shaking his sleek hand. "You're Billy's son. I probably should remember you."

"No, I'm the youngest of the family ? you would remember my older sisters."

"Rachel and Rebecca," I suddenly recalled. Charlie and Billy had thrown us together a lot during my visits, to keep us busy while they fished. We were all too shy to make much progress as friends. Of course, I'd kicked up enough tantrums to end the fishing trips by the time I was eleven.