If I start a weight training regimen to help with fat loss,will I get bulky?Is weight training that important?

In the past 2 years I have gained about 51 pounds. I am 21 and I weigh 165lbs. That wouldn't be so bad if I were 5'8'' but I'm only 5'1''. I want to get back down to a healthy weight. About 125. (I was 114, but I think I was too small. I looked "knobby" so-to-speak. When I was 120-125 l looked great.) Anyway, I want to begin a workout routine, but I don't know where to start. I know I need at least 30 minutes of cardio a day. How intense? Is it okay for me to lift weights? My fiance tells me lifting weights is important for fat loss, but I'm really worried about looking like a linebacker. So far in my family both women and men build muscle m quickly even if they start off with light weight lifting. I want to build strength too, will that bulk "fall away" with some consistent light weight lifting? I used to love to run (just for pleasure and inconsistently--stress reliever), but my thighs got bigger for a while and then they got smaller. Does weight training work the same?