Trying to move a refrigerator out of a third-floor apartment is difficult because it is cumbersome, which means that it is so heavy and bulky that it becomes unwieldy or awkward to handle. Cartons filled with books, on the other hand, are merely heavy, which implies greater density and compactness than the average load.
A huge oak dining table might be described as massive, which stresses largeness and solidity rather than weight, while something that is ponderous is too large or too massive to move, or to be moved quickly (Ex.: a ponderous printing press).
Most of these terms can be used figuratively as well. Heavy, for example, connotes a pressing down on the mind, spirits, or senses (Ex.: heavy with fatigue; a heavy heart), and ponderous implies a dull and labored quality (Ex.: a novel too ponderous to read).
Burdensome, which refers to something that is not only heavy but must be carried or supported, is even more likely to be used in an abstract way to describe something that is difficult but can, with effort, be managed (Ex.: a burdensome task). Both a package and a problem may be described as weighty, meaning actually (as opposed to relatively) heavy; but it is more commonly used to mean very important or momentous (Ex.: weighty matters to discuss).