From Longman Dictionary of Contemporary Englishweigh on somebody/something phrasal verbWORRIEDto make someone feel worried and upset The desire for peace will weigh heavily on the negotiators. I’m sure there’s something weighing on his mind. The burden of responsibility weighed heavily on his shoulders. → weigh→ See Verb table
Examples from the Corpus
weigh heavily on• Bad blood remained from the previous weeks tussle and national expectation weighed heavily on everyone's shoulders.• I felt she was holding back, refusing to release the pain which weighed heavily on her heart.• The family matter weighs heavily on him, and he is probably sensing high levels of stress and embarrassment.• By contrast, he did inherit a destructive family situation which weighed heavily on him for the rest of his life.• The beer he had been drinking steadily all day was now weighing heavily on his stomach.• Dear Parents: The responsibility for the boys is weighing heavily on us these days. 