Given that risk-averse investors demand more return for taking on more risk when they invest, how much more return is appropriate for, say, a share of common stock, than is appropriate for a Treasury bill?

Even though we know that the risk-return relationship is positive, the question of much return is suitable for a given degree of risk is especially difficult.  Unfortunately, no one is acquainted with the answer for sure.  One well-known model used to compute the required rate of return of an investment, given its extent of risk is the Capital Asset Pricing Model (CAPM).