The mass of a proton is around 900 mega electron volts/c2. The mass of two up quarks and a down quark is about 10 mega electron volts/c2.
Note that the quarks are bound by the strong interaction. The binding energy of the three-quark configuration in the proton is gigantic because the strong force is incredibly strong at short distances. This binding energy makes up the majority of the rest energy (mass) of the proton.
The proton has three valence quarks, it is true, called current quarks, whose masses are very small. But it is in the quantum mechanical regime, a bound bag of these three valence quarks and its constituents are not just that , but also include an enormous number of quark antiquark pais and gluons playing ball with each other in the proton's volume:
Read the link for details.
It is not only quantum mechanics that dominates this picture but also special relativity. In special relativity all those particles playing ball with each other have four vectors, which are additive. The total mass of the proton is the invariant mass of the sum of the four momenta of the constituents . The proton mass has been calculated in lattice QCD proving that the model of the nucleon used currently is valid.