I also live in Florida and probably experience much the same problems you do. When I first started growing I also tried to pull the weeds out, but soon found it was a losing game; you just can't do it, without some chemical help, not that I resorted to chemicals, but yanking weeds is one of those things where it could become a full time job.
Some will say that mulch will retard weed growth -- NOT TRUE!!
Mulch is only a temporary covering of weeds, emphasis on TEMPORARY and COVERING.
I started with a yard that at best was a full covering of Bermuda grass (the weeds were kept at bay with mowing) and in the shady areas I had a grass/weeds that were very sparse, interspersed with dirt/sand; it was a pain to mow, because I would kick up so much dirt. I finally decided to just totally mulch over this area with leaves I collected from around the neighborhood; at the same time I tilled the grass and mulched it over in my sunny area of the yard for a small garden. Several years later and about 75% of my yard is mulched over.
But what about the weeds? In the beginning I did attempt to yank (and mulch) them out, but I soon learned that there's no way I can win this war, despite being retired, so I did the honorable thing and admitted defeat -- I surrendered to the weeds.
But, overtime I've learned to love the weeds and found that they do serve an important function, such as providing habitat for the pollinators. And they're not as invasive as they seem, once you observe their life cycle, many of them are only here in the colder times of the year. I now don't see any plant as a weed, until I ID it and see how it fits into the ecology. Grass is now my main weed that I weed out.
However, there is one exception, the Spanish Needle plant. I have a love/hate relationship with this plant, because it's such a prolific pollinator attractor for all kind of pollinators, everything loves this flower, but if you don't keep it at bay, it will take over your yard. So I do pull it, just to keep it at bay, but I allow it to grow. Although, when it does go to seed I try and put all the seeds in a very shady area, because the plant is much more manageable in those areas. BTW, most weeds are edible, including the Spanish needle.
Spanish Needle:
https://en.wikipedia.org/wiki/Bidens_alba
