Hmmmm, I try to keep weeds out of my gardens. Not that this is ever possible, but I sure try hard to not let any go to seed. Tilling in the seed heads of weeds will certainly multiply your weed problems.
Lets face it, we are going to have weeds. The seed comes on the wind in many cases. In my case it also comes in the irrigation water which travels miles in an open canal with weeds growing on the banks. Then are those that produce seed right in the garden. Yep, we are going to have weeds.
It doesn't bother me one bit to till in the weeds right along with what is left of the garden plants. Any organic matter is welcomed in my soils. I do try to remove seed heads whenever possible before tilling.
The worst kind of weeds are those that have underground rhizome type roots. Some grasses and morning glory are two examples. To get rid of these one has to about hand dig and carefully remove the rhizomes. If you till them up, you just cut the rhizomes up into smaller pieces and each piece will grow. These rhizomes should go in the garbage bin to be hauled off. Put them in the compost and they will just grow. Well, if you can spread them out thinly, somewhere, and dry them thoroughly, they can be killed. The only other option I know is chemicals, but prefer to stay away from that.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-