Exercise (weight lifting)

I have been lifting weights and walking in a hilly area (I am aerobic on the walks) for 6 months. I know that exercise is frowned upon during the weight loss period but I don’t want to lose the strength that I have gained. It took so long and was so hard to build up the strength and now I’m seeing great results and don’t want to stop and lose it. My trainer wants me to eat at least 1600 calories on weight lifting days. Any suggestions?