Put another way, weight pulls it down, thrust moves it forward, the resultant lift keeps it up, and drag limits its speed. Only rocketeers and fighter/aerobatic pilots need to really worry about the thrust to weight ratio as a constraining factor, because the vertical flight regime matters to them. From your average bugsmasher to your commercial airliner, it's not a factor (to the disappointment of pilots everywhere).
Consider that a Cessna 172 has a glide ratio of about 9:1, so it can go 9 units forward for every 9 of altitude it gives up. If that's hard to intuitively grasp, consider that it's traveling through a fluid. Surfing, even. The interaction with that fluid is why it works.
That any more satisfying?