This may seem a bit shallow, but meals are a very important part of our lives. It's no accident that while on earth, some of Jesus' most important interactions with his followers happened over meals. Something happens to us when we share food with other people. Acquaintances become friends and friends become soul-mates over shared meals. Somehow, the presence of food helps us drop our inhibitions and open ourselves to those with whom we're sharing the meal.
A healthy small group doesn't always need food, but food almost always helps a group be healthy. Especially in the early days of the group, having snacks and drinks will help immensely as the group navigates through the awkward waters of getting to know one another.
Potlucks are great and done occasionally can be very positive, but they aren't practical for the group that meets every week. The easiest thing to help facilitate food is to create a snack schedule and make sure you remind people early enough and often enough when it's their turn to bring the snacks. As a leader, you can set the example by providing the snacks the first few weeks.
Food won't bring spiritual growth. But food will help open people up to the process of sharing their lives with one another, and that will lead to spiritual growth. On it's own, food can't make a group healthy, but it can be the first element to creating a simple and successful group experience.