Estimating heterogeneous treatment effects (HTEs) over time is crucial in many disciplines such as personalized medicine. Existing works for this task have mostly focused on model-based learners that adapt specific machine-learning models and adjustment mechanisms. In contrast, model-agnostic learners - so-called meta-learners - are largely unexplored. In our paper, we propose several meta-learners that are model-agnostic and thus can be used in combination with arbitrary machine learning models (e.g., transformers) to estimate HTEs over time. We then provide a comprehensive theoretical analysis that characterizes the different learners and that allows us to offer insights into when specific learners are preferable. Furthermore, we propose a novel IVW-DR-learner that (i) uses a doubly robust (DR) and orthogonal loss; and (ii) leverages inverse-variance weights (IVWs) that we derive to stabilize the DR-loss over time. Our IVWs downweight extreme trajectories due to products of inverse-propensities in the DR-loss, resulting in a lower estimation variance. Our IVW-DR-learner achieves superior performance in our experiments, particularly in regimes with low overlap and long time horizons.