Pilot here. There isn’t one simple answer to this question.
Every pound you add to an aircraft increases the distance it takes to get airborne, and increases the amount of runway required to come to a complete stop upon landing. If you continue to add weight, your takeoff/landing distances eventually become so large that they will exceed the amount of runway actually available (or in reality, exceed a safety margin).
Maximum takeoff weight is also a concern. Yes, an empty Boeing 737 may weigh 96,000lbs, but maybe it also needs 44,000 pounds of fuel for a long flight (140,000lbs total).
Add 160 people who each weigh an average of 190lbs (add 30,400lbs), plus 100 bags that weigh 50 lbs (add 5,000lbs for a total of 175,400lbs) and now you’re over the maximum total weight that that particular plane can safely lift (~174,000lbs).
Climb performance is also degraded by weight. Numerous popular airports in cities or near mountains can become unsafe to takeoff out of, because in the event that an engine fails immediately after takeoff, the aircraft will no longer be able to clear terrain or buildings by a safe margin.
Add to all of this, the complexities of balancing the Center of Gravity of the aircraft, maximum landing weights, reduced endurance, and many other factors.
Ultimately the weight of your baggage does have a significant impact on the aircraft and it’s performance.
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