Bone, Exercise, Alendronate, and Caloric Restriction

Inclusion Criteria: * Community-dwelling * BMI\>30 kg/m\^2 or BMI 25.0 to \<30 kg/m\^2 plus one risk factor * Currently receiving routine (annual) dental care * Pre-existing low bone mass (T-score ≤-1.1 to \>-2.5 at the hip, femoral neck, or lumbar spine (L1-L4)) Exclusion Criteria: * Weight greater than 450 lbs (DXA limit) * Resides with someone who is currently participating in BEACON * Dependent on quad cane or walker; inability to walk independently * History of mild cognitive impairment or dementia or evidence of cognitive impairment ((score \<20) on Montreal Cognitive Assessment (MoCA)) * Excessive alcohol use (\>21 drinks/week) in the past month; any non-cannabis illicit drug use * Weight change ≥5% in past 3 months * Regular participation (\>60 mins per day on \> 3 days/week) in structured strength training program for \>6 months * Severe arthritis, fracture, chronic injury, or other musculoskeletal disorder that prevents safe exercise participation; joint replacement or other orthopedic surgery in past 6 months or planned in next 12 months; invasive dental procedure (i.e. extraction/implant) in past 6 month or planned in next 12 months * Osteoporosis (any of the following): Self-reported and on prescription osteoporosis medication; self-reported prior spine, hip, wrist, or shoulder fracture after age 40 (except when caused by trauma or fall from height), including atypical femoral fractures (AFF); or ≥20% for major osteoporotic fracture at screening * Uncontrolled hypertension (systolic \>180 OR diastolic \>110 mmHg) upon repeated assessments (up to 3 times) * Uncontrolled type 2 diabetes (HbA1c \>8%); dialysis or abnormal kidney function (eGFR \<45 mL/min/1.73 m2); liver disease or abnormal liver function (ALT levels 2 times above normal); anemia (Hb\<LLN); calcium above or below normal limit; uncontrolled thyroid disease (hypo/hyper) or requiring recent (past 3 months) adjustments in thyroid hormone supplementation or thyroid-stimulating hormone \<LLN or \>10 mIU/ml; vitamin D deficiency (\<20 ng/mL). * Stroke, heart attack, heart failure hospitalization, or revascularization procedure within the past 6 months; chronic respiratory disease requiring oxygen; PAD diagnosis within the last 12 months; uncontrolled angina; progressive neurological disease; malabsorption disorder; any disease suggesting a life-expectancy \<3 years; bilateral hip replacement; past or planned bariatric surgery; cancer requiring initial treatment within the last 12 months (except non-melanoma skin cancers); major vision or hearing loss; unstable gastric reflux; esophageal stricture, achalasia, or Barrett's esophagus * Daily use of growth hormones, weight loss medications, oral steroids, or diabetes prescriptions (such as insulin, thiazolidinediones, or canagliflozin); known allergy to bisphosphonates; prior use of oral bisphosphonates for \>3 months within the past 3 years; zoledronic acid within the past 5 years; denosumab use within the past year; anabolic agents for \>3 months in the last year; current use of biotin or strontium; history of 3+ years of antiresorptive therapy * Unable/unwilling to: provide own transportation to study visits, commit to study protocol (including random assignment), or adhere to data collection visits * Current participation in another intervention research study; planned out-of-town trip greater than 1 month at a time during the first 6 months of the study; unwilling to provide informed consent, including consent to access personal electronic health records; judged unsuitable for the trial for any reason by research team