I would like to highlight cuchuflete's point, which, I believe, is that the number of boxes was 'specified' (a lot of heavy boxes), which would add to a sense of completion and generate present perfect simple, while the unspecified number of boxes (heavy boxes) removes that sense of completion, and hence he prefers present perfect continuous in that context.In this context, present perfect simple (PrPS) indicates completion, that being one of the primary meaning focuses of non-progressive verbforms in general. On the other hand, present perfect continuous (PrPC) may be used here to focus on a "completed, but the effects continue" meaning. So, the answer boils down to whether the speaker is focusing on the completion per se, or on the continuing effects resulting from the completed activity.
As an English teacher myself, I'm pretty sure the writer of the question was looking for PrPC, but in real life, while the chances of PrPC are substantially higher, PrPS is also acceptable. It is true context plus the state-of-the-moment view of things that will definitively decide.