Not losing as much as I had hoped...

My starting weight was 197lbs, I'm 5'9" and female. The past month I have worked out 4-5 times per week mostly running and my diet has been very healthy and below the caloric intake in order to lose weight. In 4 weeks I have lost 4.6lbs, which to me seems like nothing for busting my ass the way I have. I understand that with my recent exercise I am probably gaining muscle and that might account for not losing as much as I would like. My question is whether running (3 miles each workout) is not an effective way to lose weight because I'm being told that it's not and I need to lift weight in order to see results. My issue is that I do not enjoy lifting as I do running, and I have no desire to gain any muscle, I literally just want to lose weight and look better. I will say though that my body does look better, and I have probably lost inches. Basically I'm just discouraged and I'm wondering if anyone (women especially) have experienced anything similar.