Excellent answer from Silverhorse btw.
What I experienced as a vegetarian for over three years: Being vegetarian is not the same as being healthy. It helps a lot, but fries, pizza's, pancakes and lots of cheese are not doing any good.
Try to reduce the rice, it is a bit limited protein source (you are eating the brown variant, are you?). Have you ever tried Quinoa? It is a protein complete source so you don't need to worry about eating grains as well as nuts on a day.
What I found a nice way to get my basic needs of proteins, fibers and vitamins is to make a large bowl of (fat free) yoghurt with muesli (the whole-food or biologic variant), mix in a spoon of linseed and put some fresh fruit in it.
Stay large on the veggies and low on the potatoes, cheese and processed grains (like bread) etc.. Allthough, use a little bit of fat when preparing your veggies, because it will give a signal to your body it is eating "real" food (you get saturated faster; sorry, could not find my source) and some of the vitamins are fat soluble, so you get an higher intake of those ones too.
It is great you don't take any alcohol, I really applaud that.
How long are you running? I just started in August and I try to slow down a little bit. Doing to much will only get you injured, you need your body to adapt especially when you are overweight (allthough, being 85 kg is just slightly overweight don't worry about that to much). Only running will eventually get you there, but with doing additional excercises you get there faster. Do some weightlifting at your gym. You have a membership there, so that must be easy. Ideally with free weights; the machines only train one muscle group and won't add the benefits of gaining a better balance and posture.
Stay away from cardio. If you are running, you don't need cardio.
Mix the way you are running. On some days you do a long run, on others a shorter with a higher pace. Do some HIIT and negative splits.
Note: This is just a laymans advise from personal experience, but being in the kind of the same process I just wanted to share it.