Atmospheric pressure varies mainly with weather and also with altitude. Because atmospheric pressure is the pressure caused by the weight of the air column, the higher we are, the smaller the height of the air above us and thus the weight of the air column is smaller and therefore the atmospheric pressure too.
Atmospheric pressure is usually given in hectoPascals and is around 1,000 hPa (this value is converted to sea level for comparison, in reality it is lower for the above reasons). This value is not small at all, it is easy to calculate that an air column weighing 10 tons lies on 1 m2! Regarding the value of atmospheric pressure, I will add that for every 10 m of altitude, the atmospheric pressure decreases by 10 hPa. This only applies at low altitudes, since air is compressible, the pressure drop at higher altitudes is smaller.
In terms of weather, high pressure is generally sunny, while low pressure is associated with clouds and rain/snow. But this is not universally true, because the weather and its changes are more related to changes in pressure, not directly instantaneous values.
I’m not a doctor but I know that some people are more sensitive to changes in pressure and can predict (or rather estimate) changes in the weather. But it is certainly not based only on the change in pressure — to forecast the weather, we need to know the development of not only pressure but typically also temperature or air humidity. Our body is certainly sensitive to all these quantities and I think that some individuals with higher sensitivity are able to tell, based on experience, that it will be rainy, for example. But it’s certainly a skill acquired over many years of experience and I wouldn’t rely too much on these estimates anyway. For example, changing the altitude by 400 m (walking up a bigger hill) will result in the same pressure difference as a dramatic change in weather. Even from this example, I would conclude that the change in pressure itself has a relatively small effect on a person.
On the other hand, the change in weather certainly has a greater effect on humans but it is also accompanied by other phenomena — in addition to the above, a change in the electric field or the amount of solar radiation that falls on the Earth.
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