There is so much missing in your question. To start with, what is your goal? Your title says it's to be able to respect the coworker. Most of the body says it's to not have to do all the work of two people. Some parts of the body say it's to improve this coworkers skill level. You really need to know this. What do you want?
Second, in your giant list of things you've tried, I see no questions at all. When the coworker doesn't finish something, or just sits there and expects you to finish it, do you have any idea why? Is it fear, laziness, incompetence, distraction, ... ? Does the coworker wish they could finish things, or wish you wouldn't assign hard things, or have any opinions about the way the two of you work together? And why doesn't the coworker start things? Is that about your process (no backlog to pick from, no written plan to review, no regular meetings about what work is left) or a more emotional reason such as fear or laziness? I don't see any signs of insight into the coworkers motivations, yet you're trying to change behaviours. That rarely works.
A piece of advice I sometimes give unhappily married people is "do what you would do if you broke up." I don't mean "date other people" but in many cases unhappy people say things like "if I left my husband, I could read a book on Sunday mornings" or "if I left my wife, I could go to the gym after work every day." I suggest they find a way to do those things without breaking up. After all, if your wife would kick you out over the gym thing, there's no loss, you were ready to leave. But maybe she won't, and maybe going to the gym will make you happier and improve the relationship.
So to apply this advice to your situation, what would you do if this coworker left the company (or was fired) but the workload didn't change? What would you do if you were truly alone on this project? You'd do the most important things first, right? You'd have some sort of plan or checklist, and mark things off as they were done. You'd warn your boss that there was too much work for the staff available (you.) And you'd do as much as you could and be proud of what you've done. So, start doing that.
While managing yourself as though you are the only person on the project, you can simultaneously try to get some help and support from the coworker. The key here is likely to be asking things. Some sample questions:
- looking at this list of tasks, are there any you think you could do alone right now?
- ok, are there any where if we do the first one together you could do the rest of the group on your own after that?
- is there a task on this list you think is important to do first? Do you think you can do it?
- what would you like to do next?
This may result in the coworker doing at least some small part of the project alone, lowering your workload from "everything" to merely "more than is fair." That would be progress and something to build on for next time.
Maybe this poor sad coworker says "no" to everything and "I don't know" and so on. Assign something medium priority and say you do not have time to work on it together. When you have the high priority stuff done and would be turning to the medium stuff anyway, check in with the coworker and if no progress has been made, pair on it for a while. Maybe you do it all in reality. Maybe you get the coworker past a rough patch and they finish it. Again, if they do, that's fantastic because you're moving from "everything" down to "too much" which is progress.
Keep asking, keep listening. Keep trying to figure out why this coworker can't start or finish things without you, so that you can help them to get to that place. Notice and enjoy the times when the coworker does pitch in. But above all, accept the reality that you are "single" on this project and should act like that. The weight is on you. Apparently you can carry it.