A weed is only a plant in a place you don't want it - otherwise, it's just a plant.  
And according to Ralph Waldo Emerson, a weed is "a plant whose virtues have yet to be discovered."
Instead of trying to rid your yard of weeds, try embracing them - then they are no longer weeds.  
So many common "weeds" feed the bees - all year long in some areas.  
In my yard, even in winter, if the day is sunny and over 50 degrees, I see bees on dandelions - one of my favorite flowers.  
Here are weeds that I see bees on in my field.  
Also, click on any link to learn about medicinal uses of these plants.
Chickweed - tiny little white flowers that have been blooming in my field at least since Feb.

Bird's-Eye Speedwell - tiny blue 4-petal flowers with a light color center.  Blooming in my field at least since early March.

Dandelions - I see bees on all year long, including winter.  They were brought over from Europe as a medicinal plant.  We've been taught to hate them, but that just shows you the power of marketing (Round-Up anyone?).  They are beautiful yellow flowers and bees love them, too.  Even when they set seed, they are lovely.
Deadnettle (aka purple or red nettle) - is in the mint family with pretty little tubular purple flowers.  It is closely related to Henbit.  Seems to be blooming all year long.  It has been blooming here at least since Feb.  The pollen is bright red.

Henbit (aka Henbit deadnettle) - is a mint with pretty little tubular purple flowers.  It is closely related to Deadnettle.  Seems to be blooming all year long.  It has been blooming here at least since Feb.  The pollen is bright red.

Ground Ivy - this is also a mint with pretty little tubular purple flowers - they have a lovely little design in the center.  Blooms here in early spring.  Currently it's mid-March, but I haven't seen it blooming yet.