Hi Graham,
I will give you my thoughts. Put the emotional or personal thoughts of your 'mate' aside for a minute. You have financial obligations like the rest of us, morgtage, loan, credid card, bills, food, running a house....whatever they are. Your first priority is to your family...even if you are single then your future family.
So where does this take me. Every job you do you split your income. Disaster! If you are going quicker than him he is holding you back and reducing your already halved income. So this is not a situation that can contimue anyway.
If you where on your own with a reliable labourer that you paid on an hourly or daily rate...there are plenty of unemployed young people who should jump at an opportunity like this. The labourer can be quickly trained to prime, mix addy, carry tiles and cut tiles & tidy up. Leaves you free to tile tile tile...$$$. Trust me instead of halving your income you will double your work rate which will double your income.
So you leave your mate in the big bad world to fend for himself...such is life, offer him some work now and again if you are busy on m2 or dayrate basis...which ever suits you.
You have got to make your own way in this life and i thik you already know what you should do. Good luck with it. If you are not overly busy then it will be easy to tell him its not working out.
I take it you are both registered as sole traders and not filing a partnership tax return? If so you would need to file winding up books before moving on as a sole trader at the year end.