Weddingbee boards

The most solid way is to lay the aisle runner over top a plywood base, the staple or glue the edges. This also prevents the women's heels from poking through the fabric.

A narrow carpet runner would accomplish the same thing.

If you want the edges to lie flat, then I would use the thin tent pegs that just look like heavy wire.

If you are ok with the edges not totally flat, you can use any weights spaced along the edge:

stones, lanterns, mason jars with flowers etc.

Remember to have the aisle where the runner is laid blocked off so guests don't access their seats from that aisle and completely ruin the aisle runner before the bridal party makes their entrance.