Good Morning,

The lift = weight and thrust = drag comes from the physics that effect the motion of things. Remember the old F=ma (force = mass times acceleration). If something is sitting still or moving in a constant straight line at a constant velocity then all the forces on it are equalized so that there is zero net force and no acceleration. To change position or direction you have to unbalance the forces and create some acceleration.

If you are flying level at a constant speed (a steady state condition) then lift = weight and thrust = drag. All of the forces are equal and the airplane tends to keep flying straight and level.

If you increase the power setting or angle of attack you unbalance the forces. Then lift no longer equals weight and thrust no longer equals drag. The airplane speeds up or down and goes up or down (what ever the change in conditions and its aerodynamics allow it to do) until the forces on it are again all equal.

When a new steady state condition is achieved then again lift = weight and thrust = drag. That is also a boring way to fly unless you are in a passenger airplane. Most aerobatic airplanes are never in a steady state condition and lift never equals weight. When looping for instance lift is greater than weight so the airplane accelerates up in a smooth way and the result is a change in the position of the airplane so that a loop is the result.

On the lift = drag question. If we measure it in a wind tunnel to get the answer (the most accurate way) for a particular airplane we find it is a curve relationship depending on the characteristics of the airplane in question but is generally shaped like the little picture I have attached. As the lift goes up the drag goes up much more. The wing itself and even the airfoild has the same kind of shape. The particulars of the shape depend on the thickness of the airfoil, camber, and most everything else that is related to the geometry of the airfoil, wing and airplane.

This kind of stuff is interesting isn't it?