Trying to be Tough - I don't know if you're still with us, I hope you are. I know there's a great temptation to just try to hide from all this and try to pretend nothing happened or you can handle it, or it's too much info, it's overwhelming. I understand that and yet I'm gonna add my own thoughts in case you check back when you feel up to it.
Your husband sounds very disrespectful and uncaring. He may be physically gorgeous and all that, and you may think you're very lucky to have a specimen, but he doesn't sounds like a nice guy or a good husband. He doesn't sound like husband material to me, I'm gonna be frank. You're a better person than he is and you deserve better. He's criticizing you not just for gaining weight - I can understand a man doesn't like it - I'm overweight and I don't like it. My husband's overweight too but I don't look for other men. That's a sleazy thing to do and it puts personal sexual satisfaction ahead of one's spouse and HIS kids. These are HIS kids too. He should not be doing this to THEIR MOTHER. Cheating with some hose bag at the gym, so gross. Maybe he's great on the outside, but not so great on the INSIDE. You can loss weight and dress better, etc, but how is he going to develop a better character inside?
From what I've read it sounds like he's criticizing not just your weight but a lot of things since you had the 2nd child. Things you can't help or control like a different body odor? WHAT THE HELL? I never heard of bullshit like that. He's looking for excuses to cheat on you because, IMO, he doesn't want the responsibilities he now has a 2x father. He's in the trenches now as any person with 2 kids would be and I don't think he likes that and he wants an escape route. He's setting you up so that he always has an excuse to cheat with some hose bag because HE'LL ALWAYS FIND SOMETHING WRONG WITH YOU NO MATTER WHAT YOU DO. This is him setting you up. It's almost like a type of grooming. Grooming you to be a wife appliance....someone who makes his life comfortable and takes care of the dirty work while he goes out and plays. He's already told you he's thinking of cheating AGAIN...but he'll tell you first. Of course.
This is what I think you should do - what I would do anyway. Well, I would have taken a blunt object to his boyish good looks, but on a practical level.....start thinking right now about how you can make your life better without him. I'm not saying rush off and get a divorce (although it's not a bad idea if you could manage it, it's probably what I would do if I could), but realize that this guy is deliberately undercutting your self esteem after having TWO CHILDREN FOR HIM and he's doing it to push you into the role of the compliant little woman at home who keeps accepting his cheating because he's God's Gift to Women. Well, he ain't and you shouldn't. You need to start falling OUT OF LOVE with this guy and YES, you can do that - focus on all of his faults and magnify them as much as possible - I'm telling you this because he's only going to get more toxic with time.
Spruce yourself up - NOT FOR HIM - but for yourself - work on losing weight, exercising, getting some better clothes, get your girl friends or female family members to help you spruce yourself up. THIS IS NOT FOR HIM. THIS IS FOR YOU - to make you feel better about yourself and so you can withstand the bullshit he's telling you to groom you into compliance. The better you look, the better you'll feel, the more opportunities you can make for yourself.
Think about what you might like to do for work or what you can do for work. Obviously 2 small kids creates limits but i can be done and maybe you need more education. There are even online programs for various things you can do. I do think counseling FOR YOU - NOT MARRIAGE COUNSELING - you don't need marriage counseling. Your husband is an asshole. There, I said it for free. You are not....you just need to build yourself up physically, educationally, and career wise. YOU CAN DO THIS. Many women have, with even more than 2 kids. You just need to have faith in yourself....and stop believing in him. He's not a good man, he's gonna get worse with time, and you need to invest in yourself, believe in yourself and you can make this happen. Do NOT put anything more into this marriage. Put your time, energy and money into yourself.
I would start with counseling for yourself - you can even do counseling on zoom calls now - and also enlist the help of your friends and family. Tell them about him if you want to, the hell with him. And start sprucing yourself up - maybe start with make-up and clothes and work towards diet and exercise. You need a mission, girl - make yourself the MISSION!!!