For PC users you can increase size via console. The size of settlements are conservative in size, so even the low spec PC's can handle it. But if you have a PC well above the minimum spec's for the game, you can increase it with little risk, depending on your spec's.
Stand in front of the workbench
Open console
Click on the workbench (you have clicked it successfully if you see the ID number displayed for the workbench)
Next you want to determine the amount of triangles being drawn for the settlement, and determine the amount of draw calls.
Type the following in console (with workbench highlighted)
getav 348 (shows number of triangles drawn)
getav 34a (shows number of draw calls)
Write the two values down on a piece of paper, or remember them in your head. My numbers for Red Rocket outside Sanctuary, was ~46000 for Triangles, and 1000 for draw calls. I doubled these numbers without noticing anything performance wise (I'll list my specs below)
To insert new values, type the following (still workbench highlighted)
setav 349 (I doubled the value to 92000)
setav 34b (I doubled the value to 2000)
Exit console.
My spec's;
CPU: i5 3570k quad core (OC to 4,0)
GPU: Asus GTX970 STRIX 4GB
RAM: 8GB KingSton HyperX
I believe I could at least triple my numbers if I wanted (and probably more). But to be sure, you can increase in smaller increments. The increase will first and foremost depend on your GPU, so if you experience lag symptoms or drops in FPS, lower the value for triangles and draw calls. And of course, use at own risk 