I stress picking them up early on, even though they weigh a lot, because that's when you need money most. You can carry a 15 lb dragon bone that's worth 500 gold, or a 30 lb iron armor that's worth 125. In low levels, when (for me, at least) the alchemist has what I need most but buys almost nothing, it's nice to be able to trade dragon bones and scales for potions and ingredients. IIRC, bones have a 500 value and scales have a 250 value, though what you'll actually get for it depends on your speech skill.
I made a whole lot of cash by locating a container near the entrance of any dungeons or caves I visited. Dump excess weight in and, if needed, make a return trip before completing the dungeon. At the end, take the high value items first, load up your follower, and come back for the lower value stuff as soon as you can. Or, invest in a horse and you can trudge over to him and fast-travel regardless of weight.