The only time you need the thrust to exceed the mass (better term than weight) is if you want to go vertically upwards, i.e. like a space rocket or a military jet at an air display.
In steady flight, mass is balanced by LIFT not thrust. The opposing force here for thrust is DRAG
Hope this helps a little.
Try searching this site for 'Principles of Flight' or Google for oddles of good stuff.
Cheers,
The Odd One