There are many factors that go into stock market prices besides the strength of the dollar. With interest rates this low, there's hardly anywhere else to invest one's money.
Correlation does not imply causation. True economic strength would result in both higher stock prices (reflecting stronger companies) and a stronger dollar (reflecting increased demand for those companies' goods and services). One needs to take the stock market prices in the context of the actions of the Federal Reserve and despite the weakness of the economy.
