1999 Dodge Ram 1500 4X4

Looking to see what the max size tire I can sit on my stock 16" rims is. I do not mess around with tires that much, can I get 33's on it - also do not want the wheels sticking outside of the fenders too much...

 

The limitations represented by the rim itself have more to do with width than diameter. You can go as tall as you want as long as it's not too wide for the rim. Probably about 4 or 5 inches wider than the rim is the max that you'd want the tire to be, even less for a skinny rim like 6.5". The tire manufacturer will list acceptable rim widths for each tire size. Stick with manufacturer recommendations and you'll be fine.

My 12.5" wide tires on 9" rims stick out an inch or two if I had to estimate.

 

Without some lift, 33's will rub in various places. General rule of thumb for lift vs. tire is 3" for 33's, 5" for 35's. If you don't off-road, or do much variable terrain, you might be able to do 33's without lifting.... but, it'll be tight.