Using the improved U(1) and SU(2) slave-boson approaches of the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B 64, 052501 (2001)] that we developed recently, we study the doping and temperature dependence of superfluid weight and spectral function and discuss our finding of the universal scaling behavior of the pseudogap. It is shown that at low hole doping concentrations x and at low temperatures T, there exists a propensity of linear decrease in the superfluid weight ns∕m* with temperature T, and a tendency of doping independence in the linearly decreasing slopes of (ns∕m*)(x,T) with T in qualitative agreement with the experimentally observed relation; that is, (ns∕m*)(x,T)=(ns∕m*)(x,0)−αT, where α is a constant. It is also demonstrated that there exists a boomerang behavior; that is, both Tc and ns∕m* increase with hole doping concentration x in the underdoped region, reach a saturation (maximum) at a hole doping above optimal doping, and decrease beyond the saturation point in the overdoped region, in agreement with μSR measurements. Based on our improved SU(2) slave-boson approach to the t-J Hamiltonian, we further investigate the doping and temperature dependence of the spectral function and discuss our theoretical finding of a scaling behavior of the pseudogap. In addition, we discuss the cause of the hump and quasiparticle peak in the observed spectral functions of high Tc cuprates. It is demonstrated that the sharpening of the observed quasiparticle peak below Tc is attributed to the bose condensation of holon pair, in agreement with observations. From the predicted ratios of the pseudogap Δ0 to both the superconducting temperature Tc and the pseudogap temperature T*, i.e., 2Δ0∕kBTc and 2Δ0∕kBT*, respectively, as a function of hole doping concentration x, we find that there exists a universal scaling behavior (sample independence) of these ratios with doping, by showing a nonlinearly decreasing behavior of the former; that is, 2Δ0∕kBTc∼x−α with α∼2 and a near doping independence of the latter; that is, 2Δ0∕kBT*≈4–6.