Potentially huge weather effects, depends on how you're adding atmosphere, etc, etc.
One effect, would be that any low-orbiting satellites would like start experiencing friction and would have to be raised in orbit, the remainder would start crashing. You would ground all human space flights until spacecraft are redesigned; they would need (probably) more than double their current thrust capacity (longer time to get thru more atmosphere carrying more fuel - 90%+ of all fuel is used to move the fuel needed to the height and speed at which it needs to get used).
You might also be stranding (or killing them on re-entry) all orbiting astronauts, as re-entry now has twice as much air to get thru (and perhaps frictional heating lasts a lot longer?).
Mass of the Earth 5.972x10^24 kg
Mass of the Atmosphere 5.1480×10^18 kg
Mass of the Earth after 5.97200515 × 10^24 kg (negligible increase)
Would have an insignificant impact on gravity, as barely nudges the overall mass.
Depending on what you're adding (ozone?), and if you add it all at sealevel, could result in a higher percentage of things which are more stratified in the upper atmosphere (currently). These are trace amounts of the bulk of the atmosphere, but would probably be considered pollutants. This would take some detailed science to figure out. As a single example, the current ozone is stretched so thin that we have an ozone hole, if you double the atmosphere, the amount you need to cover the sphere at that density more than doubles. So you would end up vastly increasing the ozone hole - even if you were injecting the ozone at the appropriate layer of the atmosphere. If you inject it all at sealevel, at an average temperature, it will take time, and have temperature changes to get where it needs to go - however the need for it to be where it needs to be will be immediate. And, AFAIK ozone is not available in Oort-cloud material, so is your space-station manufacturing this?
Also, this is a huge space station to process so much material, so quickly. I'm assuming it has antigrav, as it would have to be well out of a LEO yet needs some means to transport its product?
There are a lot of potential answers, which all depend on the choices you make with how you're adding the gases and particulates.