Using an effective (coarse-grained) thermodynamic potential describing the excess free energy of mixing of a polymer solution and fitting its parameters to measured critical point data, we obtain the "hump" epsilon(tau) of this potential in the two-phase region (tau being the reduced distance from the critical temperature T of unmixing). For 30 different systems (varying the degree of polymerization r as well as choosing different polymer-solvent pairs) it is shown that the data are reasonably well represented by a power law, epsilon(tau)=epsilon(tau)tau(zeta). While mean field theory implies zeta=5/2 and scaling theory zeta=3 nu+beta approximate to 2.22 (using Ising model exponents nu approximate to 0.63,beta approximate to 0.325), the "effective" exponent extracted from the data mostly falls in between these limits (zeta(eff)approximate to 2.4). since the interfacial tension satisfies a similar power law, sigma(tau)=sigma,tau tau(mu) (with mu=3/2 in mean field theory or mu=2 nu approximate to 1.26 in scaling theory), we also consider a relation between interfacial tension and free energy hump, sigma(epsilon)=sigma(epsilon)epsilon(phi). While mean-field theory implies phi=3/5 and scaling theory phi=2(3+beta/nu)approximate to 0.57, the empirical exponent lies in the range 0.5 less than or similar to phi(eff)less than or similar to 0.6. we present estimates of molecular weight dependencies of critical amplitude prefactors epsilon(tau)sigma(tau)sigma(epsilon) and of related quantities for many different systems. We also discuss whether the critical amplitude combination (epsilon(tau)/B-tau)(2/3)/sigma, where B-tau describes the coexistence curve {phi(coex)((2))-phi(coex)((1))=($) over cap B(tau)tau(beta)} is universal. Contrary to some theoretical expectations, our data imply that this combination is not universal, and hence it cannot be used to predict interfacial tensions from equation of state data.