"Bear hard upon" is a phrase that means to exert pressure or weight on something or someone. Synonyms for this phrase include "press heavily," "weigh on," "crush," "oppress," and "burden." These synonyms are often used interchangeably to convey a sense of intense pressure or stress causing discomfort or hardship. The phrase "bear down on" can also be used as a synonym for "bear hard upon." It is important to note that the usage of these synonyms depends on the context in which they are used, and their level of intensity can vary depending on the situation.