"以沉重的步子行走" can be translated into English as "walk with heavy steps" or "trudge along".
"Walk with heavy steps" directly conveys the idea of moving with a slow, labored, or weighed-down gait.
"Trudge along" implies walking slowly and with effort, often due to fatigue, a heavy load, or a difficult situation, which also captures the essence of moving with heavy steps.
Both expressions are suitable depending on the context and the desired nuance.