Your QQ plot bears a strong resemblance to that of a t distribution with 2 degrees of freedom (plot based on 40000 observations):
A t(3) and a Cauchy with sample sizes of 40,000 don't look as much like your QQ plot as the t(2), but note I'm not saying this is evidence that your error distribution is a t(2) or is even well-approximated by one. The point is that your distribution is very fat-tailed indeed.
With the t family, the optimal estimator of location is redescending, meaning, heuristically, that the weight applied to extreme observations goes to zero faster than the observation value goes to infinity. This means that extreme values receive less weight than with the Huber estimator, for which absolute values greater than the parameter $k$ have weights that, in effect, go to zero as fast as the observation value goes to infinity. In the Wikipedia page for "Robust statistics", a little over halfway down, is a graphical comparison of the influence of values on the Huber (called "Winsorizing at 1.5") and Tukey biweight (a redescending estimator.) A little farther down is a plot of the influence function of the optimal estimator for various t distributions.
Consequently, with this data, I'd not use the Huber $\psi$-function at all, instead setting
psi=biweight in your call to
rlm, and accepting the fact that a lot of your observations will have little or no influence on the final estimates. Note, as @Macro observed in the thread to the other question, that this isn't a question of identifying and downweighting outliers, this is actually trying to get somewhat close to optimal estimates given your errors really do come from a very fat-tailed distribution - no outliers required or assumed.