I do not disagree with most of the things said above, but that is only looking at one side of the story.
Perhaps we should look at what may be MF's husbands view of the situation. He married a lively young woman, presumably with lots of interests. You have been married 9 years and have three children assuming they have all been born during the marriage the youngest is probably only 2 or 3. While children always changes the way life goes, you have on your own admission
I have put on weight, which I think is a big problem for him, although he won’t admit it. I used to have time for the gym and the hairdresser, and I used to look lovely - now all my time is spent looking after the home and children. I have no time for myself.
I actually have some sympathy (note, only_some_) for your husband. You do not say you work. I assume you do not. He comes home each night to an overweight woman who is harassed by small children and probably has nothing to talk about but children and domestic matters. I can understand, to a certain extent why (he)finds my desire to show him affection suffocating and finds me boring.
He may want to do something to change the situation, but given that both of you are non-confrontational doesn't know how to broach the subject. I am sorry to say but while excess weight would never stop me loving someone, as far as I am concerned it is a bit of a passion killer.
I think that the first thing you need to do is gain some agancy over your own life. By posting on GN you are starting to do that, but I feel that much of the advice being given is very negative and assumes the only answer is to leave your husband and separate your children from their father - and I am not sure life will be much better foryou as a single mother. I think that before your do that you should see what you can do to resolve the problems you have.
The first thing is, as others have said to go to your doctor, speak about depression and ask for counselling. I think that getting counselling, which will mean you needing to organise an hour when you can visit the Counsellor, will be the first step of a new life you control.
While the first years with young children can be overwhelming, for you that must already be easing a bit. Your eldest child must be at school now and the others at nursery a few mornings a week. Next time they are all off your hands, instead of trudging home and immersing yourself in housework, go for a walk. The exercise will do you good. Find out where the nearest gym is, possibly one with a creche, where you can start doing a class again. This will get you out of the house and meeting other people.
As you take more control of your life through counselling and getting exercise, you will then be able to address your weight problems, You were slim, not that long ago. You can make decisions about not snacking, not eating what the children leave. The moment they stop eating douse their plates with washing up liquid. You won't eat the remains if you do that!
Once you are slimmer and fitter and less depressed you will have more confidence and feel in more control of your life. You will then be in a better position to address the real problems in your marriage. I quote:
I don’t have any input into our finances at all. I don’t even know how much he earns. I can’t plan birthdays or holidays or buy birthday presents.
Marriage is the coming together of two equal individuals and where all the financial power is in the hands of one member there is no equality.
It may be in the end that there is no way out but separation, but I would still start to see if your relationship can be revived and put on a better footing. If you can return to your old self, you will feel much better and can then address the imbalances in your marriage. If your husband will not do that then you need to look atother options.