Why could nineteenth-century chemists not directly weigh atoms and molecules?

In the nineteenth century, chemists were unable to directly weigh individual atoms and molecules because these particles are invisibly small.12

While scientists could measure the macroscopic quantities of substances involved in chemical reactions, they lacked the technology to isolate and weigh single particles. Consequently, early chemists like John Dalton had to rely on deducing relative atomic weights by examining the ratios of combining weights of elements in chemical compounds. This approach was complicated by the fact that chemists did not initially know how many atoms were contained within a molecule, leading to inconsistent systems of atomic weights and chemical formulas across Europe.1234

It was not until the work of chemists like Stanislao Cannizzaro, who revived Amedeo Avogadro's hypotheses, that a consistent and robust system for determining atomic weights was established. By 1870, scientists were finally able to estimate the masses of atoms in grams using the kinetic theory of gases and other methods.413