What a nob.
I'm so sorry OP.
It doesnt really sound like it would make that much difference to your life if you split up, you do everything anyway. When are you supposed to find the time to shop and cook and eat healthily, and get enough sleep, and relax (being well rested and not stressed is essential for losing weight).
He is being horrible, for these reasons -
Your baby is young and giving him children is the reason for your weight gain
You are so busy looking after the children, which is facilitating his job.
Being grumpy with someone is a horrible and manipulative way to get what you want. He could have sat you down and voiced his concerns and said it in a much gentler way eg said he was concerned about your health and asked what he can do to support your weight loss if you want to do it, rather than being nasty. Instead he sulked like a toddler til you brought it up. Since when was this an effective way of encouraging someone else?
It's all about him. He wants you to lose weight not for your physical or mental health, not for the kids, but so he can have something nice to look at.
You are not responsible for someone elses unhappiness (that doesnt mean that peoples behaviour doesnt affect others, so when you are deliberately nasty to someone else, like your husband was to you, obviously you have to accept you are making them feel like shit), don't you think it's a bit odd that his whole mood is based on someone else in his life's appearance?
Lastly....being overweight is a tiny part of someones life. He is placing disproportionate importance on this. Literally the only thing it could affect for him is how much he fancies you and therefore your sex life which let's face it with three young kids, is a small part of the relationship (compared to the time you're not having sex). It doesnt affect how you communicate, how compatible you are, your shared goals, your parenting etc etc - all the million other things that come together to make a relationship.
My husband is overweight (much more than you are, which is an average size in the UK). Do I sometimes hope he will lose weight? Yes. Do I ever say anything about it? Not at all, as firstly he is aware of it himself and doing so would only make him feel bad. And my body has changed after children as well so it would be hypocritical. And lastly, how he looks is just a small part of our overall relationship - how he treats me and our children is much much more important to me than how he looks.
You can lose the weight if you want to, but do you think your husband will lose his ability to act like a cruel selfish toddler? How can he be horrible to you over this? Literally anyone you speak to will say it would devastate them if their partner said the same.
If you do go to Relate, make sure you bring up how he did this - how he sulked and how he said it in a cruel way.
I would also be very wary of the future with him. What if you had an accident and were disfigured in some way? What if you have cancer and have to have chemo with the associated side effects on your appearance? Would he act like a dick again? Or leave? What happens when you get older and your body changes shape?