Carbon Dioxide accounts for about 0.04% of the atmospheric gases, while Oxygen accounts for about 20%. The rise in CO2 is actually extremely small when comparing the percentage composition of the atmosphere and so has almost no sizable affect on the global atmospheric pressure. Even if it did affect global atmospheric pressure then this pressure difference should not affect the weather to a degree that would be noticeable in comparison to the temperature difference compared to global warming.

As to our ability to breathe, our body will attempt to generate more haemoglobin to hold more oxygen, just as plants will reduce their pores to take in CO2, this should be easily governed by most normal bodies. Despite these possible changes the rise in CO2 in the atmosphere has a larger influence on the global temperature and ocean dwelling animals than on land dwelling animals. Oceans absorb CO2 and become acidic, reducing oxygen levels and killing aquatic organisms. While we may get a breath of oxygen every day, the average herring will perish and die.

it is important to note that while the rise of CO2 in recent years is extremely small, the rise does affect global temperature more than you would expect from such an 'insignificant' gas.

The air weighs about 14 pounds per square inch. Using 4 pi r squared for the surface of the earth, 4000 miles radius, 1760 yards x 3 feet x 12 inches, and 2240 pounds to the ton, the atmosphere weighs 5 x 10e15 tons.

There appears to be 1000 gigatons each of oil and coal reserves today. I would estimate we have already used (wasted?) a third of the total. So we might expect eventually to add 3 x 10e12 tons of carbon to the atmosphere. Do not count the oxygen within the CO2 - it's already in the air.

We might therefore expect total fossil fuel carbon to increase the weight of the atmosphere by 1 part in 1700, if none of it is reabsorbed. So 760 mbar might become around 760.5 by 2100, when all the carbon has been extracted.

You might worry more that "carbon capture" systems (which capture CO2 not C), if 100% successful, are going to lock away 8 x 10e12 tons of atmospheric oxygen, because every 12 tons of C combines with 32 tons of O2.