Your diet is healthy, so is Eatthecake's including the butter. Here's what the NHS site say about sugar.
^The kind of sugar we eat too much of is known as"free sugars". Free sugars are any sugars added to food or drinks, or found naturally in honey, syrups and unsweetened fruit juices.
Many foods and drinks that contain added sugars can be high in energy (measured in either kilojoules/kJor calories/kcal) and often have few other nutrients. Eating these foods too often can mean you eat more calories than you need, which can lead to weight gain and obesity.
Adults are advised not to eat more than 30g of free sugars a day, which is roughly seven sugar cubes. Children should have less than this^.
And for carbs,
Starchy foods such as potatoes, bread, rice, pasta andcereals should make up just over a third of the food you eat, as shown by theEatwell Guide. Where you can, choose wholegrain varieties,or eat potatoes with their skins on for more fibre.
I've just checked the Wheat Belly guy and found limited research to support his being able to sell many books and what research there is is dated and not in his field of expertise.
Stone ground wholemeal could be better for you, though the word wholemeal covers a multitude of sins. A wholemeal loaf made by the Chorley Wood method (in an hour) and sold by all supermarkets will have all sorts of additives which will not be in those I bake at home.
If you could make your own bread, soups etc., that would certainly be healthy but if you're both working not so easy.
Reducing portion size will help.
Interpret the word exercise as broadly as you can. From simple exercises in your own home, to walking more, not using lifts and so on.
Certainly add veg to DH's meals and maybe frozen peas to yours.
All the best to you both.