Well obviously the lightest computer with the longest battery life is the Apple MacBook Air, as far as I know. But with Apple product's it's like this, you hate them or you love them, so if you're an Apple fan and your brother can afford to buy u an Apple computer, then this should be it. But I still recommend you to visit some sites and check out some reviews that will help you decide. I'll give you a link of a great site, that was very helpful when I was buying myself a new laptop, and it may help you as well.
Here's the link:
http
/pickbestbuy.com/category/computers-accessories/