Hard to tell what's going to happen because when you remove the chickweed and scarlet pimpernel it'll be hard to avoid uprooting any little cornflower seedlings.
Do I take it that the soil/compost had been in the pot since last year and was being re-used, so that the weed seeds had got in there from last year? Unfortunately that's a false economy - it would have been better if you'd put at least a few centimetres of fresh compost in the top of the pot before sowing your seeds, so that they didn't have to compete with weed seeds 