It depends on whether the lawn weeds being cut during mowing have gone to seed. While it's not necessarily a significant problem to have weed seeds returned to the lawn along with grass clippings (especially with a mulching mower, since the clippings are finely cut, which probably destroys some seed in the process), since there are probably ungerminated weed seeds already present, ideally weed seeds should be removed and either thrown out or hot-composted. ("Cold" or passive composting won't kill weed seeds, but "hot" or active composting should.) Lawn clippings by themselves are best left on the lawn using a "mulching" mower (the type that cuts the debris more finely and deposits it back into the lawn), but if it's too inconvenient to switch between bagging and mulch-mowing areas of lawn, picking one technique to use in all areas is probably fine. For very hard-to-eradicate weeds (Canada Thistle, say, or Bermudagrass), bagging is the safer choice to avoid a buildup of more weed seed, but for more nuisance weeds (Crabgrass, Bittercress, etc.), skipping bagging and just mulch-mowing should be fine.

Miri