Background and objectives: Obesity and anxiety and/or depression are common comorbidities in patients with chronic obstructive pulmonary disease (COPD). For doctors treating COPD, cough has a certain importance as a symptom. The purpose of this study was to figure out how obesity and anxiety/depression may influence the subjective assessment of cough. Materials and Methods: 110 patients with COPD participated in the study. The patients were divided into two groups, one including obese patients, and the other including patients with normal body weight. All patients filled out the hospital anxiety and depression scale (HADS) questionnaire, evaluated the severity of their cough by using visual analogue scale (VAS) on the 1st and 10th day of treatment, and underwent a 12 h cough monitoring with a special cough monitoring device both on the 1st and the 10th day of treatment. Results: The severity of anxiety according to the HADS in patients with COPD and normal body weight was significantly higher than in patients with COPD and obesity, corresponding to 9.25 ± 1.37 and 8.20 ± 1.18 points, respectively (p = 0.0063). The patients with normal body weight and obesity, but without anxiety and depression, subjectively noted an improvement in their well-being on the 10th day of treatment (p = 0.0022, p = 0.0021, respectively). In subgroups with normal body weight and obesity with anxiety and/or depression, the mean values for VAS on day 10 did not change significantly (p = 0.1917, p = 0.1921, respectively). Also, patients from the subgroup with normal body weight and anxiety/depression had a significantly higher assessment of their cough on day 10 than obese patients with anxiety/depression (p = 0.0411). The VAS values correlated positively with the actual amount of cough (r = 0.42, p = 0.0122 and r = 0.44, p = 0.0054, respectively) in patients without anxiety and/or depression, while in patients with anxiety and/or depression, there was an inverse correlation between VAS values and cough (r = −0.38, p = 0.0034 and r = −0.40, p = 0.0231). Conclusions: It is important to diagnose and treat anxiety and depression in patients with COPD for a better prognosis and higher efficacy of medical treatments. While treating such patients, it is preferable to use a cough monitoring device for objective assessments, since the patients may exaggerate or underestimate their symptoms.