for a weed free bed, try this. rake level and firm the bed about 21 days before you need the land for carrots, after 14 days most of the annual weeds will have germinated. cover with light-excluding fabric for 7 days, this will kill all the weeds. don't disturb soil again!
to sow carrots, don't 'draw' a drill with a hoe, just lay a broomhandle on the surface of land, press in firmly, water just the bottom of the depression thus formed, sow seed sparingly, backfill wih seived compost and firm in. water after 3 days with a fine rose if it ain't rained. ;)