The concept of relative atomic weight originated from measuring the combining weight of hydrogen with a certain element. In the simplification process H was taken as unity (18th, 19th and 20th century). For example from combining weights of hydrogen and oxygen, one can show that the weight of oxygen is almost 16 times more than H. Chemists did not have any means to measure absolute masses.
Now when Aston invented the mass spectrometer in 1940s, he also measured atomic masses. Aston's book is available here https://archive.org/details/in.ernet.dli.2015.205751/page/n14
1) As per my understanding, a mass spectrometer can measure the absolute mass based on charge-to-mass ratio. Provided we know the charge on the ion which is usually one, one can determine the absolute mass without any regard to chemical principles, purely on the principles of electricity and magnetism. I am wondering how come the current masses measured by chemical means turn out to be almost the same, in terms of numerical values, as measured by an independent instrument such as a mass spectrometer. For example, O-16 isotope is still 16 by MS measurements?
2) Why don't we quote absolute atomic weights given that modern FT-Ion Cyclotron MS can detect extremely delicate mass changes?