Following is the response from DHS Research & Data Analysis Director, Tom Pullum:

I assume you are talking about the latest Pakistan survey in the PK71 files. Yes, most children were not weighed at birth, including almost all home deliveries. For "not weighed at birth," m19 is coded 9996. There is also a code 9998 for "don't know." Those codes must be excluded from any analysis by including "if m19<9996" in the estimation command or (as you say) you can construct a binary code that is, say, 1 for usable values and 0 otherwise, and then include something like "if condition==1" in the estimation command.

I have to say that I did a quick check of the difference between public and private hospitals in this survey regarding birth weight, and there is so much dispersion in weights that the means appear not to be different. However, I encourage you to proceed. It's an interesting research question.