AF330:
No, for balanced or steady state flight the sum of the vertical forces must be zero and the sum of the horizontal forces must be zero. In other words, the forces must be equal and opposite to cancel each other out:
Lift = Weight, and
Thrust = Drag
But as FCeng84 said, that's only one part of the problem, because the Lift/Weight and Thrust/Drag forces normally don't line up with each other. That difference causes rotational moments that tend to pitch the aircraft either nose up or nose down. The horizontal stabiliser's job is to balance out those rotational moments to keep the aircraft in a steady state.
The following link has a basic explanation of the forces and moments in straight and level flight:
03 - Straight And Level - X-PPL - Learn to Fly - X-Plane.Org Forum
As FCeng84 suggested, if you want to learn more about aerodynamics there are plenty of excellent text books available. One that's been around for a very long time is called 'Mechanics of Flight' by AC Kermode.