Cost of 2 stroke:: Depends on how deep your pocket is..
Any 4 stroke 50cc is going to be a underperformer. A Suzuki LT50 is better running but no suspension.
If I was to have a kid that I knew was going to be into riding for many years, I'd get a DRR 50. They can be made into 70cc when needed. Dual a-arms with real working shocks. A lil money up front but it'd last for years.

 

Have you checked the timing? May be out 1 tooth causing it to run well with no load.. Also check the rear end something may be binding up. ALso if you have a fuel filter pull it out and run direct filter may be to restrictive, may also have a partial plug in the fuel tank or system someware Or dirty tank that is putting dirt in the needles as soon as you start