I think the food stock in the fridge does go down by a small amount each time a peep eats food cooked on the barbecue. I'd imagine their 'fed meter' goes up by a similar small amount, but I've not noticed. Another thing is that only adults and teens can cook on the BBQ if they are dropped on it. Kids will shake their heads. At the BBQ party event mentioned by Aviatrix above, though, they'll all join in.
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To err is human; to arr is pirate.