I presume that you don't want to actually start WeeWX at a given time but rather you want your rainfall stats to be from 0700 to 0700 daily rather than midnight to midnight? If so that can't be done without substantial changes to the WeeWX code base. If you search this forum for 'rain since 9am' you will find a number of related threads and you will find one or two WeeWX extensions that can be used to display rainfall since a given time. From memory these extensions only give you rainfall from 0900 (or whatever time you set) for the current day, all historical aggregates, eg rainfall this week, this month, this year are still midnight to midnight based.
Gary