Why is CO2 more likely to dissolve in a basic solution than an acidic solution?
A simple way to think about this is as follows (assuming we are talking about an aqueous solution).

The dissolution of $\ce{CO2}$ in water is followed by three chemical reactions:  

$$
\begin{align}
\ce{CO2 + H2O &amp;&lt;=&gt; H2CO3}\label{rxn:R1}\tag{R1}\\
\ce{H2CO3 &amp;&lt;=&gt; HCO3- + H+}\label{rxn:R2}\tag{R2}\\
\ce{HCO3- &amp;&lt;=&gt; CO3^2- + H+}\label{rxn:R3}\tag{R3}
\end{align}
$$ 

Now the more basic the solution becomes, the further reactions \eqref{rxn:R2} and \eqref{rxn:R3} (\eqref{rxn:R3} becomes significant at high pH) lie to the right as hydroxide consumes $\ce{H+}$. As reaction \eqref{rxn:R2} depletes $\ce{H2CO3}$, reaction \eqref{rxn:R1}  is also forced to the right. The net result is more $\ce{CO2}$ residing in solution (dissolved) as the solution becomes more basic.