There is not much difference between the household, individual and domestic violence weights, since there is almost a one to one correspondence of respondents to households (all women 15-49 for individual questions and one woman per household for domestic violence questions). The difference lies in the response rates, which given that they are more than 90% in Peru and do not differ much by area, do not affect the results. I would just use the individual woman's weight, v005 for the domestic violence questions.
Shea

In spite of not knowing what API and IPV ( can you please clarify) are, the number of cases for the numerator are the same (about 1655 or so), given the percentages below. Therefore the difference is in the denominator only and is not the result of differential weighting. Could it be the difference between currently married and ever married women?

The Domestic Violence questionnaire applies only to one woman per household. It was answered by 17299 women 15-49 out of 23888 women respondents 15-49, 72.4%. Obviously, there should be fewer currently married women than ever married women. I looked up the API results, they match the report for ever-married women (12,842 weighted). Using the same percentage currently married among ever married respondents (84.8% from table 5.1 of the report), and applying that to the ever-married with DV responses, I get .848*12842= 10893 currently married women. So the IPV in the last 12 months should be about 12.9/.848=15.2%.

Best regards,
Shea