Use this phrase when talking about someone ordering or serving more food than they can eat. At the buffet, her eyes were bigger than her stomach; she couldn't finish her second plate.
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Metaphoric Usage
The phrase can metaphorically describe taking on more tasks than one can manage. He had his eyes bigger than his stomach with three projects due on the same day.
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Cultural Caution
In some cultures, using this phrase might be seen as rude or critical of someone's eating habits. Careful when saying her eyes are bigger than her stomach; it might offend her.