What supports the column of mercury inside the glass tube of a barometer?

Atmospheric pressure will support a column of mercury $760$ $\text{mm}$ high. See this old answer for further details. Because pressure is measured $\text{force per unit area}$, typically, the mercury column will be designed to be thin so as to minimize the volume of mercury. Even given the disadvantages and hazards of using mercury in the laboratory, many inorganic labs retain mercury columns for pressure measurement.