I have seen three ways to circumvent the building limit for settlements. Those being the "scrap weapon on ground" exploit, console commands, and a mod. Is there a "best" one? As in, does one hinder performance/stability/etc. the least?
The size budget is a polygon count designed to keep your frame rate steady by preventing you from building massive and overly complicated settlements. The size limit and current size used are actually attributes against the workbench in the settlement itself and differ between settlements.
This is calculated based on the number of objects in the settlement in combination with the size and complexity of the objects. More complex objects have a higher polygon count and as such use more of the budget. Scrap contributes to this limit so you could "fill" a settlement and then go around destroying all of the broken beds, cups, chairs, etc and have more budget available to build more.
This means that the performance hit is caused by drawing an additional quantity of items - all methods that "increase" the maximum number of objects you can build in your settlement will have a hit on performance because your machine has to draw more objects. The amount of performance hit you experience will be down to the platform you're playing on and how well the game was optimized on that platform or the specification of your hardware (PC), rather than the method you use to increase the value of a couple of variables in game.