Onee-san is cute and makes me laugh, but undoubtedly very unnerving with her obsession as well. I think I'll potentially really like this story, as long as the boy keeps his common sense about him and properly tsukkomis her as necessary. I'm not sure how good the author will be at giving a backstory, but it could certainly make a great story if they pull it off.
Also, I feel like he should just take her money and manage it for her. If he wants to keep her from hurting herself, he's going to need to take charge.
...anyway, I like it so far. It's too short to decide if it's good or not for now, but there's a ton of potential here.