With recent advancements in deep learning models for image interpretation, it has finally become possible to automate construction site monitoring processes that rely on remote sensing. However, the major drawback of these models is their dependency on large datasets of training images labeled at pixel level, which have to be produced manually by skilled personnel. To alleviate the need for training data, this study evaluates weakly- and semi-supervised semantic segmentation models for construction site imagery to efficiently automate monitoring tasks. As a case study, we compare fully-, weakly- and semi-supervised methods for the detection of rebar covers, which are useful for quality control. In the experiments, recent models, i.e. IRNet, DeepLabv3+ and the cross-consistency training model, are compared for their ability to segment rebar covers from construction site imagery with minimal manual input. The results show that weakly- and semi-supervised models can indeed approach the performance of fully-supervised models, with the majority of the target objects being properly found. Through this study, construction site stakeholders are provided with detailed information on how tp leverage deep learning for efficient construction site monitoring and weigh preprocessing, training and testing efforts against each other in order to decide between fully-, weakly- and semi-supervised training.