The broad-faced sac spider is a black-headed, one- or two-inch (2.54- to 5.08-centimeter), white-bodied type of spider. The arachnid in question (Trachelas tranquillus) has a dark brown head that can look or photograph black and a grey abdomen that can look or photograph off-white. The female is bigger than the male, by anywhere from 0.08 - 0.2 inches (2 - 5 millimeters).
Presently there are over 40,000 types of spider classified. You will have to be more specific in your description
A garden orb weaver probably
It depends on what species you desire, and what you consider huge. In my opinion the male Hobo Spider has a pretty large abdomen. However when comparing most male spider's abdomen to the female abdomen, the answer might as well be no.
The only shiny fully black spider with a round abdomen that I have seen in that area is the juvenile black widow. Their hourglass can be difficult to see when they are small but they quickly grow quite large and their red hourglass making is very pronounced on the underside of their abdomen. Always err on the side of caution with venomous spiders.
I think what you have described is a brown recluse and or wolf spider, nonvenemous
Black and yellow patterns on back. Large oval shaped abdomen. Females can about 20mm and males can be about 7mm.
Depending on its size, the spider with tan and brown striped legs and a large white abdomen might be an orb weaver, a common house spider, or even an orchard spider. There are a huge variety of spiders with this description.
The kind of spider that is large 3 inches black and fuzzy with white stripes and found in the Bahamas is a tarantula. These tend to hide most of the time, but they may come out when it rains or if they are disturbed.
White tailed spider very dangerous and toxic