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to grumble; to be unsettled; to grizzle
赤ちゃんが眠くてぐずっている。
The baby is fussing because it's sleepy.
天気がぐずついて洗濯物が乾かない。
The weather is unsettled and the laundry won't dry.
子供がおやつを欲しがってぐずり出す。
The child starts fussing wanting a snack.