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Do I need a bigger exhaust?
Will bigger exhaust help horsepower ?

This is a good question, the truth is, there is more then one answer. It depends on what engine you are talking about.  Some examples are small and 2- cycle engines they need some back pressure to keep them running. Most cars and trucks can benefit from exhaust up grades, but with many cars or trucks it will not be a noticeable difference. Aftermarket exhaust parts can also be a styling or sound upgrade by changes to the visible parts of the exhaust like the exhaust tips.

It is all about flow and size when you have a 90 and it is just bent into a 90 it has ripples in it. This slows or creates turbulence in the exhaust flow. The other kind of bend is called a mandrel bent this leaves the pipe smooth in side and out. All things in the exhaust line have reason but slow the exhaust.   The more free flowing the exhaust is the more HP and MPG you can get.

Free-flowing exhaust systems may maximize peak horsepower by reducing or eliminating back pressure; this is typically accomplished by making the path as straight as possible, using a consistent diameter throughout the system. Most V8 or V6 cars or trucks today have a H-Style Pipe where there is a perpendicular connecting pipe, resembling the letter H or have a X-Style Pipe or X-Pipe where the exhaust pipes temporarily merge, resembling the letter X. The section of tubing between the catalytic converter(s) and the rear muffler on cars that have two parallel exhaust pipes. Performance mid-pipes often have a perpendicular connecting pipe or the pipes temporarily merge. This is to equalize the pressure in both exhaust pipes.
Resonators are sections of exhaust pipe that expand to a larger diameter and allow the sound waves to reflect off the walls and cancel the out. Resonators are mostly used to reduce raspiness and popping. They do not produce much back pressure. If you take a look at my videos on how to put dual exhaust on a BMW 540i you will see I drilled a hole in the resonator and now I have two pipes coming out of it and running to the back of the car.

BMW is one of the few cars I have had that made a HP improvement that I could feel on a stock HP engine. BMW go's to a lot of trouble to make their car quiet. I would guess the muffler weighs 80 pounds or more. Cutting off the muffler and making it dual exhaust makes a difference. You can always do a exhaust up grade for the sound and looks this is why I did my BMW I was surprised when I could tell the HP increase.

The catalytic converter slows the exhaust, you can buy high flow catalytic converter but it is one thing if you take off you might end up in trouble with the law. The same go's for muffler you can all kinds of hi flow and hi claims about how good their muffler is. And some people do with out the muffler. This way depends on your local police and neighbors. Most places have sound laws.
If you look at my videos I did a lot of upgrades to my Dodge cummins.  I knew I was going to do the exhaust. When I checked most suppliers where selling 4” and 5” with and without the muffler.  So I did some checking and found;  3” that comes on the turck is good for 369 HP that is good enough for a stock truck. 4” is good till 467 HP, 5” is good for 1026 HP.  If the pipe is a little small it will be ok till you hit that HP, like 4” will work fine till you get over 467 HP output then at will take away HP from back pressure.
Take a look at my dodge videos to see my upgrads