Why is Acetic acid (pKa = 4.76) stronger than carbonic acid (pKa = 6.36)? In order to try and understand this, I evaluated it via stability of conjugate bases. The acetate vs carbonate ion. The only difference is what's attached to the carboxyl group, the $\ce{-CH3}$ and the $\ce{-OH}$. Both anions seem to have equal resonance structures as I think resonance mainly only happens on the carboxyl group. 

I think that because the methyl group is just larger than the hydroxyl group, it is able to better stabilize the negative charge on the molecule overall. But I also remember hearing that carbon can have a positive inductive effect, meaning it pushes electron density toward the carboxyl group, which would make it less stable. 

I originally thought that carbonate would be more stable because the oxygen would pull the electron density toward itself, making the charge more evenly distributed.

If somebody could explain with diagrams I would appreciate it. I lost access to my software that did electron modeling functions for me.
Well actually the $\mathrm{pK}_\mathrm{a1}$ for carbonic acid at 25 °C is 3.6. The pka = 6.36 is also including the equilibrium with dissolved $\ce{CO2}$ in aqueous solution.