Nowadays, modern Earth Observation systems continuously collect massive amounts of satellite information. The unprecedented possibility to acquire high resolution Satellite Image Time Series (SITS) data (series of images with high revisit time period on the same geographical area) is opening new opportunities to monitor the different aspects of the Earth Surface but, at the same time, it is raising up new challenges in term of suitable methods to analyze and exploit such huge amount of rich and complex image data. One of the main task associated to SITS data analysis is related to land cover mapping where satellite data are exploited via learning methods to recover the Earth Surface status aka the corresponding land cover classes. Due to operational constraints, the collected label information, on which machine learning strategies are trained, is often limited in volume and obtained at coarse granularity carrying out inexact and weak knowledge that can affect the whole process. To cope with such issues, in the context of object-based SITS land cover mapping, we propose a new deep learning framework, named TASSEL (aTtentive weAkly Supervised Satellite image time sEries cLassifier), that is able to intelligently exploit the weak supervision provided by the coarse granularity labels. Furthermore, our framework also produces an additional side-information that supports the model interpretability with the aim to make the black box gray. Such side-information allows to associate spatial interpretation to the model decision via visual inspection.