This one is tricky because as far as I can see they are interchangeable in many cases without following a clear grammatical rule but at the same time they are also certainly not the same word. If you want to use them anyway, the best explaination I could give you is that "端庄" is most often seen when being used to describe women's facial features and it means they have a decent looking face(not necessarily pretty). For example, "她穿着得体，容貌端庄。" "庄重" is used to describe either an event where it means "serious" or someone's facial expression in which case it means "respectful and serious". For example, “这是一个庄重的场合。”, “他站在国旗下，神态庄重。”.

【端庄】means dignified,usually describe sb. has a pleasant appearance or graceful and dignified manner. 如：容貌端庄，举止端庄文雅。 【庄重】means grave,serious,sedate,solemn(tone) 如：他讲话语调庄重。 法官神情庄重。

简单地说，两个词近义，但前者多形容女人。

“端庄”is used to describe a person. Well, “庄重” is used to describe a occasion.

端庄 解释：表情自然大方，不扭捏做作，行为举止得体。 庄重 解释 （言语、举止）不随便：不轻浮如态度庄重 这个词汇口语中是不是很常见，希望对你有帮助~