  In this paper we study the steepest descent $L^2$-gradient flow of the
functional $\SW_{\lambda_1,\lambda_2}$, which is the the sum of the Willmore
energy, $\lambda_1$-weighted surface area, and $\lambda_2$-weighted enclosed
volume, for surfaces immersed in $\R^3$. This coincides with the Helfrich
functional with zero `spontaneous curvature'. Our first results are a
concentration-compactness alternative and interior estimates for the flow. For
initial data with small energy, we prove preservation of embeddedness, and by
directly estimating the Euler-Lagrange operator from below in $L^2$ we obtain
that the maximal time of existence is finite. Combining this result with the
analysis of a suitable blowup allows us to show that for such initial data the
flow contracts to a round point in finite time.
