Why was the Sabbath instituted in relation to the gathering of manna?

The Sabbath was instituted in connection with the manna so the people would pick up twice as much on the sixth day, Friday, in order to have enough and not have to work on the seventh day. Thus the double gathering on the sixth day supplied enough for the seventh day.

Les explains that this comes out of Exodus chapter 16, where the children of Israel had been given the manna. The Sabbath was instituted so that they would pick up twice as much on the sixth day, Friday, in order to have enough so that they wouldn't have to work on the seventh. The double gathering on Friday provided for the seventh day, tying the Sabbath directly to the gathering of manna.

Exodus 16:22

And it came to pass, that on the sixth day they gathered twice as much bread, two omers for one man: and all the rulers of the congregation came and told Moses.

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Why was the Sabbath instituted during the manna period in Exodus 16?

The Sabbath was instituted during the manna period so Israel would gather twice as much manna on the sixth day, Friday, and have enough for the seventh day without working. It regulated the miraculous provision and prevented work on the seventh day.