In order from the most 'heart-wrenching' to the least
1. Franky
His story eliminated two of the emotions I would give anything so as not to feel or experience in my lifetime: regret and guilt. I found his past the most painful to watch and empathise with and when he finally forgave himself after hearing Iceberg's words, I never felt more relieved while watching/reading One Piece
2. Chopper
Gosh, knowing that you caused your most important person's death must be tough... Added to that pain is discrimination and plain outright rejection from everyone... If I didn't relate to Franky's story more, I'd give Chopper the first place...
3. Robin & Nami
They both suffered for a long time and had to deceive everyone around them just to survive. Both women know the pain of loneliness and the fragility of having trust in someone else... They're up here because they seem the most 'breakable' if the situation arises.
4. Zoro, Sanji & Usopp
These three tie for me

Zoro and Usopp having lost someone dear to them while Sanji has to live with (a little) shame at accusing and suspecting his boss... Lol, these three are pretty straight-forward so I don't have much to say
As for Brook and Luffy, I'm still on the fence for where they rank...
Well, they clearly beat 4th place though...