Question
can the weight of tree branches be unhealthy for trees, or do the branches need to be trimmed? They are not trimmed in forests and seem to be doing fine.  

Answer
No the weight of the branches will not adversely effect the health of a tree. The branches and their foliage produce the food for the tree and a tree could not live long if the majority of the branches were cut off. Lower limbs will prune off naturally with the shade and these also can be pruned if they are a problem with not being able to walk or work under a tree. I hope this is what you were asking.