Simple RFID reader - AM demodulator not working
The large, slow amplitude variations occur because the tag must necessarily consume power from your transmitter in order to operate at all.

The data you're looking for will be in the form of low-amplitude (a few mV), fast (typically 3.9 or 7.8 kHz) square waves. You'll need a high-pass filter after your detector in order to separate the two kinds of variations.