It looks to me as if the numbers starting with 'B' are the serial numbers of the applications. So your applicant first applied for relief in 1870, and the application was No BB66300. This application was duly processed, dealt with and closed when complete. The, in 1872, the same person applied again, and the new application was given serial number B77489. Rather than start a separate new page for the applicant, the clerk has added the new application to the same page, so that the whole of the applicant's history is all together, rather than being kept in chronological order. (Some parishes did keep them in strict chronological order, with a reference 'See No xxxx' to make the link to the applicant's previous history.)
The 3.44.149 could refer to a different set of records, for example the Register of Poor as opposed to the Register of Applications.
The procedure was roughly that you applied for relief, and your application was considered by the parochial board. If you were is desperate straits, the Inspector of Poor had authority to give emergency relief to tide you over until the board could consider and decide on your application. Once the board agreed that you were eligible for relief, you were placed on the Register of Poor, which usually recorded what payments or other things (like food, or rent, or shoes, or clothing) they gave you. If your situation improved and you no longer needed relief, or if they offered you some form of relief and you rejected it (most commonly people would reject the offer of being taken into the poor house) they would 'strike you off the roll'. If you then applied again, the board could reinstate you on the roll, and deal with you as then appropriate. So a successful application would generate two records - the application and how it was determined, and then the entries in the roll, or Register of Poor.