I'm 6'5" tall and about 235 pounds. I am bigger than most paddlers that I know. I'm bigger than most people I know. It has it's advantages and disadvantages. I hit my head on things a lot, I have trouble finding clothes that fit properly. I also have trouble with riding smaller boards.
Archimedes's principle, physical law of buoyancy, states that any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant force, the magnitude of which is equal to the weight of the fluid displaced by the body. What this means in simple terms (trust me I'm no physicist) is that an immersed object is buoyed up by a force equal to the weight of the fluid it displaces. SUP boards are generally either classified as "displacement" hulls or "planing" hulls, though both shapes displace water.
A really simple formula would be: Board Weight + Paddler Weight + Gear Weight must not be equal to or greater than the weight of the water being displaced.
You don't really think about this number or the weight of the water (about 8.35 pounds per gallon). What you do think about is how the board feels under your feet. A board with a higher volume will generally be able to carry more weight without becoming unstable. Other factors impact stability as well, like board length, board width, rail shape, bottom shape, fin shape, water conditions, wind, etc.
What all of this means is that bigger people generally need bigger boards. "Bigger" can be longer, wider or thicker than normal. Maybe someone like me could ride a 10' x 36" x 6" as easily as a 17' x 28" x 5". Of course these board are going to be designed for different purposes with the 10 footer being better in white water or surf while the 17'er is going to be must faster and will track better in flatter conditions. As an extreme example, let's take me at 6'5" (high center of gravity) and 235 pounds riding a drop-stitch constructed inflatable that measures 10'6" x 32" x 4". It sounds about right until you consider the construction. This board is constructed with lots of nose and tail rocker so even unweighted, only about 9 feet of the board touches the water so now the actual (water touching) dimensions are 9' x 32" x 4", quite a bit smaller but probably do-able. Now, let's add me the rider to the board; all 235+ pounds to the center of the board. Because of the construction, the board will bend in the middle so now only about 8 feet of the board touches the water. In addition to being less buoyant, the board is not going to handle well and tracking will be difficult and slow.
What I'm trying to say is that we should consider these factors when board shopping. When just starting out, get a board that fits you and the conditions in which you paddle.