Grow in this sense is a linking verb.
6 a always followed by an adjective [linking verb] : become
▪ He suddenly grew pale. ▪ He had grown tired of hearing about their problems. ▪ She grew fat due to her lack of exercise. ▪ He's worried about growing old. ▪ These diseases are growing more common. ▪ We have grown accustomed to his angry outbursts.
Merriam-Webster's Learner's Dictionary
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