Right I have read your post.
And a few pages of comments.
So im sorry if I have missed anything out.
So his mother passes (not your mum) he inherits and doesn't share thats cool I wouldnt expect my half brother (paternal half brother - same dads different mums) to share as its not my maternal half brother (same mother different fathers).
Now your father dies (both your dads) but all he leaves is debt again that's cool happens sometimes nothing you can do unfortunately.
Now your mother dies everything she has now is hers as she obviously had to clear the debt of your father off.
Whatever she had is yours, but if she told him she would give him half then i would stick to my mothers wishes and give him half because there wasn't a will do you believe this is what she would have wanted if so then do it.
But wait this is where the story turns and becomes interesting...
Your grandparents have now passed on after their daughter your mother.
Now what your actually inheriting from here is maternal grandparents will (nothing at all to do with Your half brother) your mother passed before them so she doesn't inherit into her estate it goes directly to her descendants which is only you. So he's not entitled to anything as it was never your mother's to begin with...
Because in that will it would state...
I wish for XYZ AMOUNT to go to my daughter (your mums name let's call her) Betty but if for any reason she departs before us this share should go to any descendants of our daughter Betty.
So even legally it was never your mother's money. Its yours.
If you wish to gift him some then that's your perogative with how much, he should be grateful for anything that you may give but bot expect anything.
Hope this helps and clears up anything. Sorry if I have missed any details.