Assuming you’re getting adequate fiber and micronutrients from other sources, there’s nothing inherently wrong with eating a lot of nuts/nut butter. As for whether you will “get overly chubby,” that will be determined by your total caloric intake, not the amount of calories derived from any one source. But be forewarned: Because it is both very tasty and very calorically dense, it’s all too easy for caloric intake to get out of hand if one eats PB ad lib.
All that said, I would suggest that you not use nuts/nut butters as a protein source–you just don’t get enough quality protein for the ‘cost’ in calories. A tip I learned from Shelby Starnes (a prominent online trainer): For each food you eat, think of it as belonging to one of three categories: Protein, Carb or Fat. So for example, lean ground beef is a Protein, as is baked chicken breast. Yes, both have some fat (and trace carbs), but you don’t need to worry about those. Rice is a Carb–again, while there’s a bit of fat and protein in there, it’s not enough to worry about. Likewise (and here at last is the point I’m trying to make), PB is not a protein–it is a fat. And that is how you should think of it–as a fat source, not a protein source. So when you’re looking to hit your protein macros, don’t reach for the PB jar.
Finally, I would strongly recommend you eat ‘natural’ PB, as the others contain added unhealthful fats as well as sugar. (This is why natty PB has to be stirred–it doesn’t have those added stabilizing fats.) Read the ‘ingredients’ on the label; if it lists anything other than ‘peanuts’ (and maybe ‘salt’), put it back.