In GA you got Bermuda grass so you are good to go. Bermuda grass is the most aggressive grass around.
It may be to late to eradicate your weeds because you probably have a lot of weed seed in your soil. But you can work on your yard for next year.
first step - get a weed sprayer. You can get this for about $8
Then get a bottle of weed killer that is safe for Bermuda grass and only kills the weeds and not the grass. Most brands are good
Start spraying your yard to kill all the weeds. In about a week you will see brown patches which is good.
next get a few bags of milorganite or the Lowe’s brand Procare and apply this to your yard. This fertilizer is organic and can’t burn your yard.
With the weeds dying you Bermuda grass will start to spread if you keep it cut Every three days.
normally you would apply a pre-emergence in February to prevent weeds from growing. It is kind of to late for that. So you will have to spray your yard a few times this summer.
By July you will start to see a really healthy developed yard. Your weed problem will be cut down by 70% with a few spots popping up here and there