The child does not want to leave the house

A 5-year old has emotional eating issues. She says she is and acts as she is hungry all the time, even though she eats 5 times a day (two meals when she eats as much as she wants and two snacks in-between). Because she is overweight now, we try to encourage her to exercise more. Grandma take her to the beach, which is a great exercise for her, and she used to love it. But she hates it now and refuses to go. It seems like she is afraid of leaving the house. We think it is because she wants to be around the food all the time, and even though we don’t give extra snacks to her anymore as we used to, she still wants to stay home now. She does not want to exercise and does not enjoy being physically active.
Things are getting worse and she needs to lose weight, but she also needs to move more and not be afraid of leaving the house. What can we do to help her lose weight?