Here's a slightly different take - why use BMI at all?
Kronmal RA. Spurious correlation and the fallacy of the ratio standard revisited. Journal of the Royal Statistical Society. Series A (Statistics in Society). JSTOR; 1993;:379–92.
Spurious correlation refers to the correlation between indices that have a common component. A 'per ratio' standard is based on a biological measurement adjusted for some physical measurement by division. Renowned statisticians and biologists (Pearson, Neyman and Tanner) have warned about the problems in interpretation that ratios cause. This warning has been largely ignored. The consequences of using a single ratio as either the dependent or one of the independent variables in a multiple-regression analysis are described. It is shown that the use of ratios in regression analyses can lead to incorrect or misleading inferences. A recommendation is made that the use of ratios in regression analyses be avoided.
If you do decide to use BMI as a continuous variable you'll need to check your regression model carefully for violations of assumptions - BMI often has a (very) nonlinear relationship with whatever else you're measuring.