Double weave can be done with 1 rigid heddle reed. Thread the reed, 1light, 1 dark in each hole, 1 light, 1 dark in each slot. In front of the reed place a pickup stick with all the top layer colour threads above it. If you tilt the reed, you see sheds. If the reed is in up position, you have the first light shed on top. Pick up with a knitting needle or pickup stick. Lay the pickup stick flat again. Slide the knitting needle over the pickup stick.
Also, if the reed is in up position, the bottom shed is the first dark shed.
If the reed is in down position, you have the second light shed on top, and the second dark shed on the bottom. For the dark bottom sheds, you slide the knitting needle under the pickup stick.
For the light layer on top, lift the knitting needle and throw the light weft through that shed.
For the bottom layer, push the knitting needle down and throw the dark weft through that shed.

This is basic doubleweave. With a second knitting needle you can pick up a pattern. Pick up dark threads and add the sheds of the light top layer to the dark pattern threads; then throw the light weft through the combined shed.
For the bottom layer, pick light pattern threads below the warp and add them to a dark bottom shed, and throw the dark weft.