If you are training properly then you will see a difference in the next seven weeks, especially if you are also eating in a healthy fashion.
If you can, go three times a week as suggested, always leaving a day in between for your muscles to recover. Do a 10 minute warm up to raise your heart rate, get your muscles moving and then do your weights first. Make sure you are lifting heavy enough, if you can do more than 12 reps with good form then you need to put the weight up. Only rest for about 60 seconds in between sets. Lifting heavy weights will really raise your heat rate, trust me, and the 60 seconds rest gives your muscles time to recover but is short enough to keep your heart rate up. Once you have done your weights, then do 20 minutes of high intensity interval training so for example if you were on the treadmill you would jog for 2 minutes, sprint for one minute and so on, then cool down and stretch. Try and have a high protein snack or meal within an hour of finishing.
Do you just use machines at the gym? Do not under estimate exercises like weighted squats and lunges, the plank, step ups, prone jackknife, prone cobra etc.
If you are going to 'diet' then only cut about 300 calories a day, anymore than this will actually have the opposite effect than the one you want as the aim with weight training is to increase your metabolism and when you severely restrict your diet then you are slowing it down. Do make sure you are eating enough protein throughout the day so that you are 'fueling' your muscles, they won't get stronger without it!
Sorry, long post, hope there was something vaguely useful to you in it!