heavy 普通用词，指重量或体积大大超过同类物体，常用作引申，多指精神上的重压等。
weighty 多指实际上而不是相对的沉重，引申指严重或重要。
参考例句
1. Obesity is a weighty problem. 过度肥胖是严重的问题。
2. This was a subject most of the people thought weighty . 这是一个大多数人认为严肃的题目。
3. But at least they were casualties of weighty conflicts over their country's future in the European Union (EU). 但是至少他俩都是关系到英国将来在欧盟地位的重要冲突的“阵亡”功臣。
英英解释
adj.
1. having relatively great weight; heavy
2. powerfully persuasive
3. of great gravity or crucial import; requiring serious thought
4. weighing heavily on the spirit; causing anxiety or worry
5. excessively fat
