I have a Jack Russell named Riley and on his most recent trip to the vets I was told that he was overweight. Now I know it's hard to judge the correct weight for a Jack because you can get so many different types, but the vet said he should be anywhere between 6-8kgs and he weighed just over 9kg. She said his shape should have a broad chest and a prominent waistline, which at the time he didn't have. So I went home and made some changes; I cut down his food to just below what they recommend for his size breed so he could lose some weight, cut out almost all his treats and started letting him off the lead in our local park so he could run rather than just walking next to me (I walk him for 30 minutes - 1 hour every morning depending on how busy I am that day), and he is always full of energy and runs around for the whole time we are out, and we never feed him human food anyway because I know it can be really bad for dogs so that didn't change. So after a month of these changes, and sticking to them very strictly, I noticed that he did look slimmer and now does have a prominent waistline, but when I took him back to the vets he had gained 0.8kg rather than losing any, so now he weighs a little under 10kg. My partner seems to think that he has gained weight rather than lost it because of the increased exercise and thus increased muscle mass which is making him heavier, or the fact that he might be still growing (as he is only 11months old), but surely to gain almost 1kg in a month is ridiculous? Especially when he's between a small and medium breed? I want to know if there are any issues I need to e made aware of or any other tips I may find useful to get him to lose more weight.

I would say it is the increase in muscle mass. He is at the teenager stage right now where his body is starting to go from flabby puppy to muscly adult.
As long as he looks physically fit I wouldn't worry too much about weights. The weight charts at my local vet say one of my dogs should be 8kg and he is pushing 12kg... He is in beautiful condition.

If you are still concerned about his weight adding grated carrot to his food is a good trick. Carrot contains barely any calories and makes them feel full so they are still satisfied and not missing out on full meals, but not gaining any unwanted calories.

What are you feeding him? A lot of brands of food, such as beneful, advertise they are a weight loss food.. but they're not even close.

Grocery brand foods are very high in fat. If you want him to lose weight, you need to get him on a better food that has higher protein.