Hi and welcome Veronica 
In terms of your weight, to social services it's all about how your health might impact on your parenting and future health and life expectancy. Being overweight is not a barrier, but it will be considered along with any other risk factors you have (so being very overweight and a smoker and having Diabetes, is much more problematic than simply being overweight if you are otherwise healthy). If you can show that you have been actively trying to lose weight, then I think that would be okay. People are approved to adopt with high BMI's.
How old are your 2 DC's? There does need to be at least a 2 year age gap between your youngest child, and any new child, so to be approved for a child aged 3-6, your DC both need to be over 8/9. My personal opinion is that bigger age gaps can often work out better than smaller ones
There are children of all aged up to about 10, who need adoption. Children aged 4+ are hard to place and less prospective adopters feel able to adopt a school aged child. The same is true of children with special needs, who are hard to place no matter how old they are.
However, it's very important that the age of child you ask to be approved for, and what special needs they have, is an age and level of need that you are comfortable with and want. There are a lot of things to consider when adopting an older child, and if you want a younger child, then don't feel guilty for a minute about asking for that. Ditto special needs. It's about you as a family, your DC and what you are all going to be able to handle as a family. And mostly it's about the new adoptive child, who needs to go to a home who really want a child like them and are equipped as much as possible to deal with their needs, whatever they are
My dh is very worried that we would be taking a child away from a childless family
This is not how adoption works, and is something your Dh needs to put out of his mind. For a start, there are many more waiting children than there are parents approved to adopt. But the key thing to remember is that adoption is not primarily about the waiting families and giving parents their child...it's primarily all about the child, and finding the right family for a particular child. So let's say the local authority have a healthy child aged under 1 who needs adoption, and the social workers have to choose between two families, a childless couple and a couple with 3 older children. They will choose the couple whom they think can meet the childs needs the best. That may well be the couple who already have children. Nothing has been taken away from the childless couple, the child who needs them is still out there somewhere.
Hope that helps. Feel free to ask us anything and hope you find the board helpful