Nothing. The problem is that your compost just like mine does not get hot enogh to kill off all the seeds that are either added to the compost heap or blown in from else where.
Shop bought compost is steralised so that you dont get all matter of things growing from it.

All you can do is pick out the weeds. I am forever picking out tomatoe plants that have grown from seeds that are in the compost some where.

I only use my compost for potting on and adding to the borders.
I always buy fresh compost for raising seed.
Hope this helps.

Are you putting weeds with seeds on in to your compost? as they can then start to grow when you use it - if they have not got hot enough to be destroyed in the making.

My compost is riddled with weed seeds. I don't use it for potting for this reason but it is still invaluable in the vegetable garden.

Yes, I know what you mean Bh having nurtured seedlings only to find they are weeds lol

As the others say, if you're using your own garden compost for potting, that's not a good use for it - use it on the soil in the garden, where it is invaluable for all plants, whatever they are. this kind of compost is not potting compost, which is sterilised before sale, or produced using a hot composting system.