I am a layman in chemistry. However, if I have to choose between “mass” and “weight”, I prefer “mass” because “weight” involves the gravitational acceleration in general physics (W=m×g).
But when I was in high school, it was called “Molecular Weight”
It is said “为了避免质量和重量的混淆,所以,国际计量大会建议在科学用语中,取消重量概念。” (please refer to 28#, http://bbs.instrument.com.cn/shtml/20110712/3410991/index_3.shtml )