I've posted this chart before, and here it is again, updated. I still don't have a good explanation for why a weaker dollar is good for equity values. Maybe it's that when things look bad for the economy, it increases the demand for dollars as a safe haven. Now that things aren't looking quite so bad for the economy, the dollar slips and equity prices rise. Today's dollar slide appears to be the result of the ECB cutting their interest rate target by only 0.25% (to 1.25%), which was less than expected. The ECB's reluctance to follow the Fed into full panic mode suggests that perhaps things aren't quite as bad as is generally believed.
And indeed, I don't think things are so bad. Lots of things have bounced recently: auto sales were up in March, commodity prices are inching higher, home sales are up, the ISM manufacturing index is up three months in a row, and of course equities are up for the past three weeks.