Without a doubt, the speaker in "Digging" admires his father and grandfather. He admires their work ethic and skill. You get a sense that our speaker wants so much to be like them, even though he never will be, being a writer and all. His admiration for them seems to have begun at a very young age, and it does not let up as the speaker becomes and adult, even though he has chosen a different line of work. In fact, perhaps it's because he admires his father and his grandfather so much that he tries to be as hard working as they are, even though his work is very different. He grows up looking up to them, and his admiration shapes the person the speaker becomes in his adult life.
Because the speaker admires his father and grandfather so much, it's impossible for him to respect himself fully. He'll always be living in their shadow.
Because of the speaker's admiration for his father and grandfather, he has incorporated their attributes into his very different line of work.