I'm just going to be blunt (and I say this as someone who is currently sitting at a size 18 having lost a bit of weight and obviously still with more to go so I myself am currently fat).
Being fat will definately make it more difficult to get a job. I had done lots of interviewing (retired now) and yes sorry it would have been a black mark against you. Not to say you would definately not have been hired if you were amazing and the other candidates were rubbish. Given two decent candidates - one thin and one fat, yip the thin one would almost certainly get it.
Also another place I worked the boss (man in his sixties) on seeing one of the candidates getting out of her car said to me 'don't hire the fat bird'. So I had to do a fake interview knowing I wasn't allowed to give her the job anyway. She from memory was about a size 18-20 but short.
I am currently not working (retired I think) but in the event I had to go back to work I would be desperately trying to lose weight to get down to a 16 or better a 14 which lets be honest is not small sizes given how large the sizes are nowadays. I'm 5ft 8.
Your age will also be going against you because whilst forties is not that old - the combination of being a bit fat plus a bit old will just be too much for many employers. If you were mid forties and slim and looked healthy they may overlook your age but the two combined is just going to make it tricky.
If there is lots of jobs then your chances are better obviously. If the market is competitive you will struggle. My plan was to work at a care home if I had to go back to work as I am older than you and like I say fat myself and figured I would manage a job there as they seem to be desperate for staff and thus less fussy. Not sure if I could have done the cleaning of people etc though.
You have my sympathy. Sorry if any of this upsets you but if you know the problem maybe you can try and lose some weight though I know it is very tough.
If it makes you feel any better I have been in jobs where I almost didn't even get an interview because company told the recruiting agency 'no women' and it just so happens I was the token pretend candidate who was much better than all the males (also 30 and attractive though!). I expressed shock to recruitment agency that they had said no women and the agency female said 'it happens all the time'
Old fat blokes are also discriminated against but not to the same extent.
Black people or people with non british names are also discriminated against. I've had CV's pulled out of my pile of 'candidates to interview' as not being suitable based on this. Not by me, but others said 'not them'
It's ugly but it's the truth.
Obviously fat people do work so it is not impossible but I do wonder how many of them were thinner or younger when they were hired?
Sorry if I have upset you. I'm just a fat, old person myself who has lots of interview experience and seen how the world really is.