1)Mercury is more dense. Its relative density is 13.534 times that of water. So, to measure the atmospheric pressure, which is 760 mm of mercury you need a barometer ,with mercury, of length slightly more than 0.76 meter, say one meter to cover the special cases of some higher pressure. If you use water, you have to have the length of barometer of length (or height) 13.534 times the length of mercury barometer, which may be more than 11 meter in length.
2)Further mercury, being a metal has the shining quality which highlight its reading clear.
3)Also mercury, having comparatively lower specific heat and good conductor of heat, could come to the same temperature of the atmosphere more quickly.