Passive RFID with small size, light, cheap and range in meters for a reader
Yes, this is possible! You could use RAIN RFID (UHF RFID) using passive tags. The tags will be thin, flexible and cheap ($0.10-$0.05).

The read range depends on the output power of the reader, and the size of the tag. With a tag that has around 15cm2 area (3x5 cm or 2x8 cm) and a typical handheld reader, you can get up to 5 meter reading distance. With the tag size you require (5mm x few centimeter) the reading distance will be slightly smaller, but still a few meter.

Using the Returned Signal Strength Indicator (RSSI) value that comes out of the RFID reader you can get an impression on the distance between the tag and the reader.

A mobile RAIN RFID reader costs around $1000, but prices are expected to drop sharply in the next few years.