DNS data obtained under conditions of weak turbulence that are well associated with the flamelet combustion regime are analysed in order (i) to assess the widely-accepted linear relation between the mean mass rate w of product creation and the mean Flame Surface Density (FSD) and (ii) to investigate transport of the FSD and the role played by local flamelet perturbations in the FSD transport. While, in line with common expectations, a ratio of w/(ρu sigma) is found to be close to the unperturbed laminar flame speed S0L within the largest part of the mean flame brush, this ratio is significantly smaller (larger) than S0L at the leading (trailing) edge of the flame brush. Nevertheless, under the conditions of the present study, this difference in w and (ρu S0L sigma) can be disregarded when computing burning velocity by integrating (S0L sigma) over the flame brush, provided that sigma is extracted from the DNS data. Even in the case of weak turbulence addressed here, the FSD transport is substantially affected by the difference between local density-weighted displacement speed ρSd/ρu and S0L. This difference is associated with local perturbations of flamelet structure by turbulent eddies, with the local flamelet curvature (strain rate) playing a significantly more (less) important role in the FSD transport under the conditions of the present study. While the difference between ρSd/ρu and S0L in the FSD transport equation can be approximated with a linear function of the local flamelet curvature by processing the DNS data, Markstein lengths associated with such an approximation (i) are scattered, (ii) vary within the mean flame brush, and (iii) differ significantly from the counterpart laminar Markstein length.