The parasite is in the blood, it doesn't affect inmunity since it only attacks red blood cells, but it leads to anemia and this is that's causing his weakness. Blood transfusion is and option but it's a bit complicated since you'll have to change ALL the blood in order to truely eliminate all the parasites and it's not that easy!
Talk to your vet, I know that there are drugs used for this, one of them is Imidocarb dipropionate which kills protozoa (the parasite babesia is a protozoa), but I can't help you more than this because I'm from Argentina and dog babeosis is exotic in here, so I only know treatments for cows haha!
I'm not real familiar with this other than I know It's a tick disease....However, It's my understanding that Chemo-therapy drugs are used for treatment.......Blood transfusion should be your last option.....
You might "Google" this disease and see what you come up with.....I wish you luck....Maybe someone else can give you more info. than I have......Karla