It squeezes me with approximately the weight of an elephant sitting on my chest. But humans are adapted to this and don't notice. It helps that the insides of my lungs are being squeezed outwards by the same force. Otherwise I surely couldn't breathe.
I am indeed wrong. Air pressure is about 100kPa, which is to say 100 kilonewtons per square meter, which is about the weight of 10 kilokilograms or tonnes per square meter, and the surface area of a human is about a square meter, so the air pressure force acting on a human is about 10 tonnes, and an elephant weighs about 5 tonnes, so it's actually the weight of two elephants.