Tree instance segmentation of airborne laser scanning (ALS) data is of utmost importance for forest monitoring but remains challenging due to variations in the data caused by factors such as sensor resolution, vegetation state at acquisition time, terrain characteristics, etc. Moreover, obtaining a sufficient amount of precisely labeled data to train fully supervised instance segmentation methods is expensive. To address these challenges, we propose a weakly supervised approach where labels of an initial segmentation result obtained either by a non-finetuned model or a closed-form algorithm are rated by a human operator. The labels produced during the quality assessment are then used to train a rating model, whose task is to classify a segmentation output into the same classes as specified by the human operator. Finally, the segmentation model is finetuned using feedback from the rating model. This in turn improves the original segmentation model by 34% in terms of correctly identified tree instances while considerably reducing the number of non-tree instances predicted. Challenges still remain in data over sparsely forested regions characterized by small trees (less than two meters in height) or within complex surroundings containing shrubs, boulders, etc. which can be confused as trees causing the performance of the proposed method to be reduced.