This is relative. A file with a lot of information will be bigger than a file with less. But, in my experience, compared to other file types, SVGs tend to be smaller. Like, when they’re the same ‘designs’, my PNG files are almost always much, much bigger than the comparable SVG.
That said, you can do some things to make sure your SVG file isn’t bigger than it needs to be. SVG saves points and paths. The more you have, the more it saves, the bigger the file gets. So double check that you don’t have extra points that aren’t necessary. So, imagine you have a line that is supposed to be perfectly straight, but has more than 2 points. All those extra points are superfluous (and might mean the line isn’t actually straight when you enlarge it enough to see). Delete the extra points, and you’ll be saving less information (and your line will actually be straight). If you delete a point and nothing changes, then the point didn’t need to be there. Some programs will have a tool (called simplify, or something similar) where you can easily eliminate points without changing the look very much. And in some cases it changes the look for the better.
This goes for font choices too, if that’s part of your design. Some fonts have lots and lots of points compared to other fonts. This can make a big difference if your file size, even when you have the same amount of text. (And with that, you probably want to make sure the font you’re using is being saved as SVG-ness, not as a font. If you can change the text, it’s still a font. I don’t know how to word this. Maybe someone who understands what I mean can translate that into an actual coherent sentence)
Also, don’t use two paths (or 15) when you can use one. The specific term depends on the software, but merge, join, combine, collapse, unite, etc, whatever you can.
And, probably easiest, be sure you aren’t saving the SVG with any additional features it doesn’t need, like preserving editing capabilities or program compatibility. This is an option in some programs that can make the file much bigger. Feel free to save the editable version as a backup, if you’re worried, but save it turned off in the version you will actually cut. This goes for other file types, too. Any extra info makes the file bigger.