This might be a dumb question, but off the top of my head...
INDICATED AIRSPEED - This is what the airspeed indicator shows (this assumes no mechanical errors in the instrument and no errors in the pitot and static pressure measurements).
TRUE AIRSPEED - This is the Indicated Airspeed corrected for non-standard pressure and temperatures. For instance, both the pressure and temperature normally decrease as altitude increases. There are mechanical type "slide rules" and electronic hand calculators for determining the True Airspeed. At sea level with standard pressure and temperature, the True Airspeed and Indicated Airspeed are the same.
Would barometric pressure changes/differences (weather, as opposed to altitude) measurably affect that?
Yes. Note that in the Seattle ATC Center's radio transcripts the pilots are constantly being updated on the altimeter settings in the area they are passing through. Unfortunately, the airliner's times at various locations has been redacted in those transcripts.
Altimeters measure pressure and have a scale on the instrument that shows the pressure being measured as an altitude. In aviation, altimeters are capable of being set to a sea level pressure. What is given as altimeter settings is the pressure at a given location reduced to sea level by a standard formula even if that location is thousands of feet above sea level. So if an aircraft is parked on the ramp at a given airport at 4000 feet above sea level and asks for the local altimeter setting, the setting he is given should indicate something within a few feet of 4000 feet on his altimeter.
You cannot determine "tape line" altitude from an altimeter although there is, or used to be, a calculation called "true altitude". But the altimeter is probably the most accurate pressure measuring instrument on an aircraft.
To calculate the True Airspeed from the Indicated Airspeed, you must know the sea level pressure for your location and the temperature outside the aircraft. The outside temperature can be measured by thermometers onboard the aircraft and adjustments must be made for heating in high speed aircraft.
Here is a personal experience of mine that happened about 50 years ago near Colorado Springs, Colorado. I was flying a sailplane (glider) from a gliderport there that specialized in high altitude wave flights. In preparation for that, I had gone through high altitude pressure chamber training at Andrews AFB near Washington, DC.
My goal was to reach 40,000 feet above sea level, but I never made it. I did find the mountain wave, got into it, and climbed steadily at just a few hundred feet per minute. I was carrying onboard two sealed barographs that were temperature compensated. I dressed for the flight as much as possible, but my hands and feet turned out to be the problem areas. I had ever ventilator in the sailplane wide open just as I would have had at sea level on a 120 degree day.
Two of those ventilators were putting air directly on me and one of them had a standard aircraft thermometer with a scale from -60 to +140 degrees F in it. That gage went off the scale in the negative direct and appeared to hit a peg at what would be about -70 degrees F. I continued to climb after the temp gage pegged out, but the rate of climb slowed to about 200 feet per minute and I was freezing my rear end off. I decided to stop at 35,500 feet in the climb and when I reached that point I was going to head back down. I simply could not handle another 20+ minutes in that temperature.
Upon reaching 35,500 feet, the canopy from my shoulders back was iced over and ice was on my chest just below the oxygen mask exhale valve. I tried to retrim the sailplane but the trim tab would not budge and the dive brakes would not deploy. My only choice was to put the nose down and speed up which is what I did. I was finally able to deploy the dive brakes at about 25,000 feet and got back on the ground as fast as possible.
Upon landing, I turned the barographs over to the individual who would reduce them and certify the flight. I headed back to my motel and took a hot shower to warm up, then I went back to the gliderport and the maximum altitude was certified as 36,500 feet, which was probably the average of the two instruments. So at the highest point as I was trying to head back down, my airspeed was probably at least 1.75 times the indicated airspeed. That was also the coldest temperature I have ever been in.