莊重 (zhuāngzhòng) means serious, grave, solemn, sedate.
莊 (zhuāng) represents 莊嚴 (zhuāngyán), meaning solemn and respectful.
重 (zhòng) represents 鄭重 (zhèngzhòng), meaning serious and sober.
Example: I have a friend who always dresses properly, speaks respectfully, and behaves appropriately. She has great self-control and is well-respected. Sometimes I tell her, 你很莊重 (Nǐ hěn zhuāngzhòng).