According to the Cambridge Dictionary barometer is " a piece of equipment that measures air pressure (the force of the air) and shows when the weather will change", for example, you can see a barometer in the pic.
According to the Etymology Dictionary barometer derives from the Greek baros, meaning "weight", + -meter measure. Probably coined (and certainly popularized) by English scientist Robert Boyle (1627-1691).
Baritone, from barytonos (deep-toned, deep-sounding) has got the same root as barometer, but at the same time as isobar or barycenter. Other words with the root -meter thermometer, speedometer or anemometer.