You are missing some info, like how many reps you do, how do you eat and your lifting program in general but I will consider that you are doing 8 to 12 reps.
So lets begin...
You don't want to gain weight then, obviously your arms will grow, not like men's arm but they will grow. Maybe you can win weight by training legs and ass, muscles that women love to have, your legs and ass will grow in a still "womanish" way, but again I don't recommend to train only legs and ass, as you will look bad with a disproportionate body. I will later give you some routines and things you need to have in mind.
You could always train for strenght, doing 4 reps on each set with heavy loads, you'll get stronger and you will still grow altough a little bit less than if you continue doing 8 reps -12. Altough I would recommend you to get a personal trainer that will teach you perfect form the first months that way you don't get injured. Or you could do more than 15 reps, targeting resistance it all depends on your goals.
As I said before here is a routine that targets legs and "womanish" body parts:
First of all you can train legs 3 days a week, but the more days you train the better you need to eat, sleep and the less extreme your workouts need to be.
Monday: Legs (including ass too)
Tuesday: Abs and Obliques (If you do too much abs you will start to get rocky vainy woman abs, look above)
Friday: Abs and Obliques
We are missing back, chest and other body parts, this is a routine that most girls will use as they don't care about upper body.
Monday: Legs and Calves
Tuesday: Abs and Biceps
Wednesday: Obliques and Triceps
Thursday: Back and Chest (Chest may help your boobs to stay upright)
Friday: Legs and Calves
Remember than legs include ass too. On the second program you could train one week arms and the other let them rest, only training abs and obliques. You could also do cardio on saturdays.
This routines aren't perfect, you need to see how much and what you eat, your goals and then make a routine specially for you.
Here is the rocky vainy abs thing: