Metformin Hydrochloride, Carboplatin, and Paclitaxel in Treating Patients With Recurrent Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed high grade serous ovarian, fallopian tube or primary peritoneal cancer * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension in accordance with Response Evaluation Criteria in Solid Tumors (RECIST) criteria version (v.) 1.1; for those patients in the Phase 1a portion that are agreeable, disease must be amenable to ultrasound or computed tomography (CT) guided biopsy of a lesion outside of the target lesion; patients must have histologically or cytologically confirmed high grade serous ovarian, fallopian tube or primary peritoneal cancer * No antineoplastic therapy (eg, drugs, biologicals, monoclonal antibodies, etc) or radiotherapy within 6 months before enrollment; patients previously treated with antineoplastic therapy in the past must have recovered (ie, grade =\< 1 toxicity or patient's baseline status, except alopecia) from all treatment-related toxicities * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Absolute neutrophil count \>= 1,500 cells/mm\^3 * Platelets \>= 100,000 cells/mm\^3 * Hemoglobin \>= 9 g/dL * Total bilirubin =\< 1.5 times the upper limit of normal * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) (serum glutamic oxaloacetic transaminase \[SGOT\]/serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 times institutional normal limits * Creatinine =\< 1.5 for men and 1.4 for women * Fasting blood sugar =\< 126 * Hemoglobin A1C =\< 6.5 * Patients in the Phase 1a portion of the clinical trial must have a tumor that is deemed safe to biopsy and must consent to serial biopsies and or surgical resection after treatment with metformin * Patients must be minimally, status post bilateral salpingo-oophorectomy * Ability to understand and willingness to sign a written informed consent and Health Insurance Portability and Accountability Act (HIPAA) consent document * Willing and able to comply with all appointments for treatment, lab testing, biopsies, imaging and any other testing * Suitable venous access for infusion of chemotherapy and phlebotomy Exclusion Criteria: * Patients may not be receiving any other investigational agents * Patients must not have evidence of disease recurrence within 6 months of completing the last dose of platinum based therapy * Patient with current diagnosis of diabetes, or currently taking insulin, metformin, sulfonylureas, or other medications used for the treatment of elevated blood sugar * Conditions leading to increased risk of metformin induced lactic acidosis, including congestive heart failure (New York Heart Association \[NYHA\] class III or IV), history of acidosis, or daily intake of 3 or more alcoholic drinks * Use of metformin in the past 6 months * History of allergic reactions/hypersensitivity reactions to metformin * History of allergic or hypersensitivity reaction to carboplatin, paclitaxel, or Cremophor® EL * Baseline nausea \> grade 1 * Baseline evidence of metabolic acidosis, with total carbon dioxide (TCO2) of less than 20 * Patients with history of \>= grade 2 neurotoxicity or any toxicity requiring discontinuation from taxanes chemotherapy that is not resolved to =\< grade 1 * Any condition that would prohibit patient from being able to take and digest metformin, such as gastroparesis, history of malabsorption, history of baseline diarrhea, current symptoms of small bowel obstruction, current symptoms of an ileus, history of a resection of the stomach or small bowel, or history of Crohn's disease/colitis * Current alcohol abuse: patients using more than 1 standard unit of alcohol per day for the past 30 days; a standard unit of alcohol is defined as a 12 oz beer (350 mL), 1.5 oz (45 mL) of 80-proof alcohol, or one 6-oz (175 mL) glass of wine * Uncontrolled current illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or breast feeding * Systemic infection requiring IV antibiotic therapy within 14 days preceding the first dose of metformin, or other severe infection * Diagnosis of or treated for another malignancy within 2 years of enrollment; patient with non-melanoma skin cancer or carcinoma in situ of any type, are not excluded if they have undergone complete resection; patients with a history of stage IA endometrial endometrioid carcinomas are also not excluded * Diagnosis of primary central nervous system (CNS) disease or carcinomatous meningitis * Patient has symptomatic brain metastasis; if patient has asymptomatic brain metastasis, must have: * Stable brain metastasis for 2 years documented radiographically. * Be without any neurological dysfunction that would confound evaluation of adverse events * Women of child-bearing potential (WOCBP) are not eligible for the study; since the standard of care for ovarian cancer treatment is total abdominal hysterectomy and bilateral salpingo-oophorectomy this is not thought to exclude patients who otherwise might want to participate