Five years ago I had a similar experience with an 11 yr old boy, he told me later that we had "bonded" the first day we met.
In my case the stepfather was clearly not fond of him, but it was not until 4 months later when I returned all the boys clothes and toys to his mother that I learnt that she gave our friendship her full approval. But I am 73 yrs old.
Would it be possible to limit your friendship a little so that you can observe the reaction of the mother and her boy friend?
I have never needed to tell my YF that I love him, though I have told him that I will always be here for him.
I still see or hear from him every day and I think I always will.
I hope you are able to find out his mothers feelings about your friendship and that you are as lucky as I have been.
I am also sure that your young friend feels just as empty as yourself when missing a weekend or two and that his mother will appreciate your friendship.