Chronic obstructive pulmonary disease (COPD) is a lung disease where early detection benefits the survival rate. COPD can be quantified by classifying patches of computed tomography images, and combining patch labels into an overall diagnosis for the image. As labeled patches are often not available, image labels are propagated to the patches, incorrectly labeling healthy patches in COPD patients as being affected by the disease. We approach quantification of COPD from lung images as a multiple instance learning (MIL) problem, which is more suitable for such weakly labeled data. We investigate various MIL assumptions in the context of COPD and show that although a concept region with COPD-related disease patterns is present, considering the whole distribution of lung tissue patches improves the performance. The best method is based on averaging instances and obtains an AUC of 0.742, which is higher than the previously reported best of 0.713 on the same dataset. Using the full training set further increases performance to 0.776, which is significantly higher (DeLong test) than previous results.