Sunshineonrainydays I was screened for CBT but told it was appropriate for what I needed. I do use CBT strategies to manage my responses and expressed feelings etc but it hasn't really changed how I feel inside.
As for my bf now, I've told myself all of those things about him. That he has been single for a good few years and he is quite content to be single. He said it took quite a while for him to 'give up' part of his life for me and to factor me into his plans etc. Which I get. I've been single for a few years too and, when you have your life the way you want it - friends, hobbies, work, down time etc - all mapped out and it works for you, it requires a change in mindset to accommodate someone else.
So, whilst I think he was content to be single, he wasn't happy and what he really wants is someone to share his life with.
Again, yes, i know it says more about the people who said them. I understand all of that which is what i mean by i know it in my head but it hasn't changed how i 'feel'.
He spent a lot of time being the third wheel in friendships with other couple and I think its nice for him to feel that that isnt the case anymore - has someone to go to parties, events, gigs etc with. Things he always did, but wasn't truly comfortable doing alone.
As for the other questions, I understand they were rhetorical but they are things I've considered. He isn't often physically demonstrative. He can go for a whole evening and maybe only touch me once or twice, doesn'treally kiss me spontaneously very often or put his arm round me. But I know from reading on here that a lot of people aren't physically demonstrative and that doesnt bother me as such. He asks to see me, he doesn't cancel on me, I get invited to things with his friends, the relationship doesn't revolve around sex, he refers to me as his partner/girlfriend but generally indirectly.
I enjoy being with him. It's easy - we talk a lot and silences are comfortable and sometimes we'll just get on and do our own thing when we're together for a weekend. Which I'm comfortable with.
Bbq1 tbf, some of his friends have said so too. Not directly, but things like, "we're so glad he's with you. He deserves to he with someone lovely who'll treat him well. He's brought dates to things before but its obvious he's only with them because of their looks and they've not been right for him..." that type of thing.
Why are you confident that you wouldn't be his true choice of partner? Why, even if you lost weight (in your mind as weight is not a barometer for attractiveness btw)would you not be perceived as attractive? because, ideally, I think he probably saw himself with someone slim, with a good body and who is beautiful. Like most men, I guess. Someone who'll look good in a bikini on the beach. That sort of thing. Not someone who he has to justify being with to himself because I've got a 'nice personality' 
I am aware that my perspective on this is somewhat skewed. My parents put a huge amount of emphasis on looks. My dad left for someone who was, essentially, a younger version of my mum. The first time I met her, she was wearing almost the exact same outfit I'd left my mum in her house wearing! Similar hair cut, similar interests etc just younger.
I have had at least two 'relationships' end because the man wanted, or found, someone younger than me.
And I wouldn't disagree that he is quite fussy - I think he was probably looking in all the wrong places - women who were young, slim and beautiful... which is why I feel that he is 'setting' now, having realised he doesn't have the pulling power he might once have had
I feel bad saying that now, like I'm doing him a huge disservice he's actually a very nice man.