Pin it down - remove the pins while sewing.
If the fabric is slippery or wants to really slide, baste it first.

forgot to add - Are you holding the fabric taut in front of and in back of the needle? That helps a lot.

That sounds like a presser foot adjustment problem to me.
I'm not familiar with featherweights - maybe the manual will help. Here's some info I got from sewing.about.com

Pressure Adjustment - Parts of a Sewing Machine
From Debbie Colgrove,
Your Guide to Sewing.
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What the Pressure Adjustment Does:

The pressure adjustment sets that amount of pressure that the presser foot will exert on the fabric. Downward pressure on the presser foot, holds the fabric between the feed dog and sewing machine foot. The amount of pressure would need to vary if you were switching between light weight sheer fabric and multiple layers of denim for the machine to feed the fabric.

When to make adjustment to the Amount of Pressure:

If you find that the fabric will slip when the presser foot is down, you need to increase the pressure on the presser foot.

If the fabric is held so tightly that the feed dog is unable to move the fabric, decrease the amount of pressure on the presser foot.