Here are two tips that make the wefts completely cover the warp in rep weave shown in the sampler in my new book, Weaving for Beginners, beginning on Page 261.
TIP #1: Increase the warp tension
Increase the warp tension by cranking the cloth beam ratchet brake. Make it
as tight as you can—when you can’t crank the beam any more you’ll know
that the warp can’t get any tighter. You might do this tensioning of the warp at
the back of the loom at the warp beam, or in both places. Just note that when
either beam won’t move, you’ve tightened as much as you can. There should
be no danger of breaking the warp if you stop tightening when you can’t
tighten it anymore using your ordinary strength. You don’t want to call in a
weight lifter to tighten it extremely, extremely tight for you.

Thank you very much for your prompt and very helpful reply. I realized that I wasn’t bubbling the weft, so that the warp threads were always visible and I couldn’t figure out why I wasn’t seeing the pattern as in the book. With the bubbling, it is working well. (Although I will need to practice so that the other side looks neater!) Thank you very much for your support, I really appreciate it.
I thought in rep weave it was the warp that showed.
How does one set up a rigid heddle loom to do rep weave for placemats?
It can be warp rep or weft rep. For warp face you would need a very fine heddle for the waps to cover or perhaps two heddles. Chck out more advanced rigid heddle weaves to see if there is something you would like. If you used very fat warp yarns to cover the weft that would be a thought.
Peggy