This is always a horrible situation to be in, and if you can't change the way you think about it then the best advice is to leave, it will damage you in ways that you cannot easily perceive.

In my advice I'm going to assume that you and this other employee are a team of two and you both work for the same person (the founder) who I'll just call the manager ok?

If you can change the way you think about it, you might find it to be a very rewarding and life changing event.

First, and this is hard I know, realize that output of the team is your manager's problem, not your problem. I can hear in the way your wrote this that you have taken on tremendous amounts of ownership of the success of this product and so you do the work of two people because the other person is not working as hard as you are.

But here is the thing, if the choice is 'not successful' and you are burnt out, or 'not successful' and you are not burnt out, take the second exit. More importantly, change the criteria for 'success' in your mind from "product" to "what you have produced." Set clear dividing lines of what is 'yours' and what is assigned to this other person, communicate those clearly with the manager and get their buy in (if they are a sociopath be sure and get it in writing).

Then you can communicate with the manager in terms of how you've been successful at getting your parts done, tested, deployed, etc. That the whole system isn't done, tested or deployed isn't your problem anymore. Can you see how that works? It is the manager's problem.

My Grandfather had a phrase that went something like "You can't plow a field with an ox and an ass." It refers to using two farm animals hitched, as a team, to a plow that the farmer would walk behind while the animals pulled it through the field. The ass (or donkey) can walk much faster than the ox, but the ox is much stronger in pulling. Since a team is hitched together, our clueless farmer is trying to get the speed of one and the strength of the other to plow his fields faster. But the reality is that they can't work together because in the harness their attributes work against each other.

Your manager needs to match you up with someone who is closer to your talents if they want to get the job done, or they have to settle for plowing with one ox.

The second thing you can do to improve things is to develop some compassion for your co-worker, who in your words, "his personal life is a chaotic mess". While you are doing lots of great work, try to imagine how you would accomplish that if one of your parents was living with you and needed you for basic things like getting in and out of bed or using the toilet. You might imagine these outside family demands to be so chaotic that you don't know what you can commit to because you can't say for sure you will have 4 or 5 hours in one shot to work on something. Now add to that stress your own co-workers judging you harshly because you aren't getting things done that you are supposed to. Guilt, responsibility, fear, anxiety, it's the full depression cocktail and unless your co-worker is super human, they are probably in a really bad place right now.

Imagine the scenario where you convince the manager to fire this person and hire someone else, and that person who is fired commits suicide because they feel like if they can't hold a job they have no reason left to live. That is an extreme case but it does happen.

So if you can change your outlook on this person from being a slacker to being a superstar who has a lot of crap going on in their life that is keeping their performance down, then start to strategize with them on ways they can help even with their otherwise over whelming life issues. Talk to them about partitioning up the work into chunks they can manage in disjointed time opportunities. Maybe have them do less technical work and more technical debt cleanup or accounting. Work with them to find ways they can contribute meaningfully and you may find you are repaid ten fold as their life gets more into balance. Be there for them, and they will be there for you when you need it.

If you can change the way you 'score' life, the way in which you see success and failure, then you can be successful in all that you do. It will help avoid the toxic cycle of blame and depression that affects so many people in startups.