So sorry to hear what you are going through 
Think you don't need these fairweather friends to be honest, especially if you have other friends who are supporting you.
If you were getting them down, a gentle word to that effect would have been much kinder than avoidance. You would then have been able to adjust if possible, fade away a bit if not.
I do agree with PP that a therapist/counsellor can be a great way to clear your head in hard times. If for no other reason than you see them regularly at the same time each week. Then it becomes possible to save all your heavy thoughts for e.g. the day before, then write them down and talk to counsellor next day, leaving you with some relief for at least a few days, then it is time to write them down again etc. This advice is to make it easier for you, not your "friends".
The good thing about hard times is that it does sort the wheat from the chaff. A couple of people I thought were good friends were conspicuously too busy to see me after my mum died. They were not a loss.
There is a place in life for casual shallow type acquantainceship friendships for fun only. That type of person would never lean on you and it is usually quite clear who they are from how they are. It's fine.
Or the kind of friend whose response to a break up is to take you on a night out to cheer you up/get drunk/go dancing/meet someone new, but who doesn't feel too great about talking it over with you/being a shoulder to cry on. That's fine, it's ok for friends to choose how to be emotionally supportive in a way that best suits their own personality. But that type of person would say something like "right, let's stop moping about here, get your glad rags on we're going out on the town on Saturday night". Also the person who might cook you a meal, do some shopping for you, help you view a house if you need to move. Some people prefer to give practical support than emotional, they might be better at that or think that you need that more.
So, as long as it doesn't leave you totally isolated, view how these people are acting as a way to make space for more important things in your life.
Anyway, take care of yourself and don't waste any thought or anguish on these people.