University students (especially first-years) not only have to cope with their academic curriculum but also issues such as being away from the home environment and living independently for the first time. Those who do not adapt quickly to these new conditions are likely to be susceptible to physical and psychological vulnerabilities. The present study surveyed first-year Bangladeshi undergraduate students to investigate their weight status (i.e., the prevalence of being normal weight, underweight, overweight, and obese) and the prevalence of depression and associated risk factors. A cross-sectional survey was conducted among 404 first-year university students (aged 18–23 years) residing at a Bangladeshi university. The participants completed a survey examining socio-demographic and behavioral variables, alongside the WHO-5 Well-Being Index. Binary logistic regression was performed to determine significant associations between the variables under examination. Prevalence rates of being normal weight, underweight, overweight, and obese were 66.8%, 20.3%, 9.7%, and 3.2% respectively. Associated predictors of weight-related problems were being female and lack of physical exercise. The prevalence rate of depression was 68.1%. There were no significant gender differences and associated predictors of depression were lack of physical exercise, unsatisfactory sleep quality, excessive internet use, and excessive reading hours. Being underweight, overweight, or being obese alongside the prevalence of depression among first-year university students were high. Findings indicate that first-year university students are a vulnerable group for some physical and psychological problems. Findings recommend the need for intervention programs, alongside adequate and appropriate supportive services for first-year Bangladeshi university students.