I recognize there are many answers already, and some very good ones:

It is true that the CO2 is also waste, and that it dwarves everything else connected to it. It is also true that you cannot always avoid flying, and in this case it is also good to minimize the impact.

I'd like to focus on what you can do if you have to take the flight. I'll use Europe/New York flights as an example.

You cannot reasonably avoid plastic waste for meals on regular flights

It is virtually impossible to commercially provide in-flight meals without single-use plastic; and there is no airline that does. Any attempt to "fix" rather makes things worse:

If the airline has complimentary meals, they'll stock at least one meal per passenger. If you don't take it, it'll be thrown away, plastic included. Bringing your own meal just adds food waste to the equation. (On budget airlines it does have an effect to not buy the meal, see below).

You could opt for business class, where they have reusable dishes, but you'll multiply your CO2 footprint that way.

Optimize your flights

The best way to reduce your footprint is to avoid as many flights as possible. For business, you may be able to combine trips - e.g. going from New York to London, taking the train to Paris and flying back from there.

You may also be able to travel less often, but stay longer each time.

Savings for taking one trip instead of two: Around 1900 kg (50%) per one-way trip.

Use the right plan, go budget, go economy

These are probably the things that help most. Budget airlines will usually use new, fuel-efficient planes and pack a lot of people. Meals aren't included; they'll only pack as much as they expect to sell (meaning that not taking the meal actually has an effect and you can avoid the plastic waste as well). Many budget airlines don't offer in-flight entertainment systems which saves additional weight.

All of this helps:

If you go to New York from London, Norwegian Air Shuttle uses new 787 planes, while British Airlines uses mostly 777s or 747s. And Norwegian fits 350 passengers into a 787, while BA fits only 215.

A "high-density" 787 flight will generate around 830 kg of CO2. A regular flight on a 747 will generate around 1200 kg; one on a 777 still 1060 kg. (A business class flight on a 777 will cause over 1900 kg).

Savings: Up to 370 kg (19%)

Use a different mode of transport, even for parts of the trip

If you're in Berlin, and have a day to spare, you could get the train to London (41 kg) instead of the feeder flight (177 kg). Or take a train to Frankfurt (22 kg) instead of a feeder flight (130 kg) and a direct flight from there.

Savings: 136 kg (0,7%) or 108 kg (0,6%)

Weight matters, but not as much as you think

Using the values from other answers, an additional bag on the NY-London route would be around 14 kg of CO2 (23 kg * 0,2 kg of fuel per 6000km = 4,6 kg of fuel, times 3). This isn't nothing, but it is isn't that much either.

Also, buying new items at your destination may be even worse: Using the formula above, transporting a 0,2 kg shirt one way will cause about 0,1 kg of CO2 to be emitted, but producing a new shirt will generate about 3 kg of CO2.

Savings for one less bag: 14 kg (0,07%)

Compensate your flight

There are various offers to "compensate" your flight through a donation. While this doesn't undo the CO2 emissions, they'll use the money on projects to mitigate your impact to a certain degree.

How much this helps is up for debate - it is certainly better to avoid a flight in the first place, if possible. However, if you cannot avoid a flight you may give this a try.