Don't try to slim down. It's a trap. Eat plenty of calories and protein, you'll need it to support the kind of hard training you need to run fast. The best 800m runner I ever personally trained with was 5'10" and ~160, with a 1:46 PB when I trained with him (and 1:45 later in his career at similar body type). The 2nd best was a 1:49 guy and he was 6' and ~170. You need POWER to run the 800, and you build that power with MUSCLE, which is HEAVY. It's as simple as that.
Your training seems okay, I like to see an aerobic focus for most of the season, and weight lifting is essential. Try to see if you can get your coach to include some explosive movements in the weight room - box jumps, cleans, and snatches are a good place to start. A speed ladder would be great to include too. The other thing you can do is start doing 6-8x100m strides after your easy runs. Treat them as a constant acceleration up to somewhere around 800/mile pace around 50-80m before a slight deceleration at the end.
I think some more mileage would help you, you're still young but 30 mpw is on the lower end to be a successful distance runner. This is where the eating really comes into play; if you don't fuel, you will get hurt trying to go higher. You need to be eating 2500-3000 calories a day minimum at higher mileage. Just make sure at least the first 1500-2000 is high quality (fish, meat, whole grains, fruit, vegetables) then the last 1000 or so can be whatever you like (most pros I know are candy fiends). This summer I would shoot to be in the 45 mpw range, with 50 as a goal for your peak mileage. Try to make one day a week 10-12 miles, with a progression towards the end based on how good you feels. Another day can be the tempo, and if you can try to get one more day to do some hill sprints - anywhere from 15-60 seconds with a slow jog back recovery, at roughly mile effort. Total maybe 8-12 hard minutes, depending on how you break it up. Don't go above 15-16, no matter how good you feel.