Basically ancient Austronesian & Austro-asiatic backstrap weaving loin looms are equipped with a circular warp. Later on following models took over flat warp-methods by the impact of other cultures. The use of a flat warp is a question of tradition; most of these loin looms, using a flat warp, can be equipped easily with a circular warp, too! Many of these Austronesian flat warp-models we find on Sumatra Island, or even on neighbouring Java Island. By the influence of incoming Indian textiles most areas of Thailand, Malaysia and Sumatra Island have changed their manner of weaving totally to Indian-style frame loom techniques. Just some areas like Palembang took over the flat warp, that combines with Indian techniques, and combined it with their traditional loin loom!
Most American loin looms seem to be equipped traditionally with a flat warp; circular method is not known.
Examples of flat warp looms
(AA = Austro-asiatic; AN = Austronesian)
As you can see, most of these loin looms listed here using a flat warp are of Austronesian origin. Looms markes with a ? are optional versions next to the circular warp tradition in its area. So, the Karen loom using a flat warp are just versions of present time under modern influence. All left flat warps occur mainly on Sumatra and Java.