Absolutely YES to the things recommended so far:
See her pediatrician first. Be SURE to get her blood sugar checked in case part of her problem is a need to keep her sugar up. And possibly see a pediatric endocrinologist to see if she has the condition --which also popped into my mind as it did someone else's -- where she never feels "full" at all.
And you and dad need to sit down, today, and list ANYthing that has changed in the past months as she has gained so fast: Stresses at home, at school, a friend moved away, school got harder this year, maybe she's being teased about her size or other things? New sibling, new house, money issues you discuss in front of her--anything?
Remember -- what seems like "nothing" or trivial worries to an adult can seem like the end of the world to a child this age; eight is an age of transition, stress and even drama for many kids, so don't discount even small changes or stresses as possible triggers. She may need some age-appropriate counseling about her relationship with food and the use of food as crutch and comfort. Don't try to do it all by yourself; get help.
And please don't treat it just as a disciplinary matter! She is not being bad or naughty on purpose; she is eating out of some physical or emotional need. Finding that need is vital or she will gain more and more and shedding it will be harder and harder.
Find things to praise about her. Even if you feel, as an adult, as if "Gee, I'm constantly praising tiny things that should just be normal!" go ahead and praise her anyway -- kids are fragile at this age. If she does a chore well, note it to her. If she does something nice for her brother, however small, thank her for it. Be sure she knows that you see her beyond her weight (because you ARE going to have to give her weight a lot of attention to get this problem solved, so be sure to engage her on other levels as much as you can so she knows there is more to her than her body).
Does she have activities and hobbies? Active things are great of course, but don't discount mental activity like Girl Scouts, school clubs or groups, things that get her outside her own head and involved with other kids who share her interests.
Yes to clearing out food in your home so that tempting foods are gone and she cannot access food on her own. Try not to make a huge deal of "locking down the food" but do end your kids' open access to pantries and fridges, period. No kid should be able to wander in and reach for a nosh on his or her own.
And one last thing -- why is she even able to eat other kids' snacks at school?? Our schools have strict "no sharing of any food, ever" policies, mostly due to food allergy concerns. See if her school has such a policy and it's not being enforced. When and where are kids doing all the snacking you mention? In classrooms? Why? In elementary my child was able to snack in class but only at very specific times of day; if that's the case here, you must involve her teacher who has her during snack and say that kids need to stop sharing snacks. This will not make you popular but it needs to stop among ALL kids, frankly. It's too bad your school does not ban birthday treats -- some parents hate these bans but they do serve a purpose; if a class of 30 kids has 30 birthday treats over the year, that is a ton of junk. Volunteer at every party (it sounds like you already do -- great for you, keep it up!).
Try to involve your child in her own health. This is where an experienced counselor, used to handling kids with eating issues/emotional eating, could be very helpful, and so could a pediatric nutritionist; get them to help you empower your daughter so SHE is interested in being healthy. Do not, do not, do not let her start to equate healthy only with being thin. Involve her in shopping and cooking and learning about recipes. But this has to be part of a whole-family clearance of junk foods (sorry, but you and dad and brother have to participate--hard, I know!). A dietitian or nutritionist can help so much. But the pediatrician, and a counselor, are the starting points.
Please update us!