My son had reflux at 7 weeks, too, and it was awful. What really tipped us off was that he cried every time he spit up. That indicated that he had too much acid in his tummy. My ped suggested many things, but what worked for us was Zantac. He would still spit up alot, but it wasn't acidic, so it didn't burn his esophagus. I was just glad he was comfortable. I am still breastfeeding him today, and he has no symptoms of reflux.
For awhile he was on Mylanta and Zantac. Then when he started cereal at 4 months, he only got Zantac. Gradually we reduced the frequency from 3x a day to 2x a day (but giving him more to compensate for losing one dose). Then we dropped the morning dose completely, waited about 3 weeks and dropped the evening dose. She said they usually outgrow it by 6-9 months, but always by 1 year. By 6 months he was eating 3 solid meals a day, so he started spitting up less. He's almost 9 months now (doing great)and hasn't been on Zantac since he was 6.5 to 7 months.
Also, you might try inclining her mattress so she's slightly propped up. My ped said you can go as high as a 30 degree angle, which is best. By the time we tried that, my son would roll downhill and wake up, so we nixed that.
Also, keeping her in an exersaucer or walker after meals might help. Just not in a position where she's sitting or her legs are bunched up because that will cause spit up.
Good luck. It will get better.