To think about the meaning of a name, start first with the literal meaning, and then second with the associated or metaphorical meaning. To "weather" something is to make it through; the expression is usually used in relation to getting through tough times, as in "The family weathered the Great Depression." "All" means just that-- all. Everything. Together with her title, her name would mean she's an old woman who has been through everything and survived, or who will make it through everything. Since the story follows Granny as she reviews her memories, we can see that it definitely applies. She's done everything. After all, this is a woman who fenced 100 acres by herself!