H., I'm a single Mom too - I have a two year old and you did my heart good to hear that your son is three and you are still struggling with it. I thought I was the oddball or something :-)
My daughter was preemie - only 4 pounds at birth - and breastfeeding was something I took very seriously. She's always been small, but eats well now - she's very healthy and I'm convinced it all helped these past two years.
We're partially weaned off - the only problem is this partial business has been going on for 6 months or so now! I thought the night time "feeding" would be the hardest for her to give up, but not anymore - I've got her going to bed on her own really well.
She can't seem to give up the first thing in the morning nursing - usually around 6am - just a few minutes of it upon waking - and the coming home from work after being separated all day nursing - that's the longest and lasts only about 20 minutes or so - it's obvious she's just reconnecting with me again after being separated all day. I've come up with ways to avoid the morning one, but the coming home at night one is just impossible it seems! I try to distract her, try to do other things - she just doesn't go for it and only wants to breastfeed for a little while when we first get home.
The only other thing that's still a bit of a challenge is when I am home with her she likes to try to get little sips here and there from me when she can, and won't stop doing that, and that's all they are - sips! But at least then I can say no and get her interested in something else most of the time.
It's just the hardest thing in the world to say no to, ya know? I could give it up easily if she lost interest, but just taking it away from her is incredibly hard to do! I'm still hoping that she'll just lose interest on her own eventually - now I'm hoping before she is 3 if not sooner!
Good luck - I totally know what you are going thru and altho I had no advice to offer, I guess I was looking for a bit of my own and loved reading everyone's responses - this subject particularly caught my attention! Just know you're not alone, H. - going thru the same thing here!
C.