The wings on SpaceShipOne were pretty light and flimsy because they didn't need to be any stronger considering how slow SpaceShipOne's top speed was. It topped out at Mach 3, and you need to reach Mach 25 to achieve orbit. Wings strong enough to handle Mach 25 would be too heavy to ever reach Mach 25; Catch 22!
Yes, and this has been well understood for decades. The basic math is simple: per unit mass, the potential energy change required to get from the Earth's surface to orbital altitude (say 200 km, or 200,000 meters) is
gh = 9.8 * 200,000 = about 2 million Joules/kg
whereas the kinetic energy change required to get from rest on the rotating Earth, a speed of about 300 m/s at the latitude of the Kennedy Space Center, to orbital speed, 8000 m/s, is
1/2 (v2^2 - v1^2) = 1/2 (8000^2 - 300^2) = about 32 million Joules/kg
So the change in velocity dominates the energy requirement, which drives everything else.
It's a measure of change in velocity (hence the delta… v…, and in mathematical terms is literally written with the symbol delta) required to reach or escape x orbit.
For example you need a delta v of approx 9.3 km/s to go from Earth to LEO. From LEO to GEO you'd need a delta v of roughly half of that. Engineers in this sense would talk about a total delta v budget of ~13 km/s and some change to achieve Earth to GEO.
The question is then how do you design a rocket that can produce those numbers? Higher delta v requirements means higher mass requirements. You'd need more propellant to produce that thrust, and more structure to house it and hardware to control it. At some point it simply doesn't work anymore because it becomes counter intuitive to keep adding more mass.
Enter the concept of staging. Staging allows you to discard your useless mass after it's done it's job. For example you might need 9.3 km/s to achieve LEO, but you might also know it's not a linear relationship so that you need more of that upfront and less of it later. In that case, rocket engineers simply designed around that and created heavy first lift stages to produce the bulk of that delta v, and then discarding the heavy structure and hardware after the propellant has been exhausted.