Following is a response from DHS Senior Data Specialist, Claudia Marchena:

To get the results published in the report, you need to take the footnotes on the published table 3.3 into consideration.

Footnote:
1 Facility is connected to a central power grid and there has not been an interruption in power supply lasting for more than two hours at a time during normal working hours in the seven days before the survey, or facility has a functioning generator with fuel available on the day of the survey, or else facility has back-up solar power.

As explained in the footnote, the column on "Regular electricity" in table 3.3, uses the following logic to get the results published:

Logic:

(Q340=1 & Q341=1) or (poschar("AB",Q343) and Q345=1 and Q346=1) or pos("C",Q343)

Further explanations for logic:

Poschar("AB",Q343) is Q343 = A or Q343 = B
pos("C",Q343) is Q343 = C

The parenthesis are essential to delimit the conditions.

Regarding the weights and how to use them, they are explained in the survey documentation, TZSP71.doc. But basically each level of analysis has its own weights, Facility in variable FACWT, Provider in variable PROVWT, and client in variable CLIENTWT.