It should support whatever size SD card, because they're all the same size. However, what will be affected is the time it takes to save each photo. The higher the capacity of the card--and the more photos you take on that card--the longer the camera will take to process each image before it is ready to take another. For that reason, and not putting all your eggs in one basket, it's best not to buy anything larger than 16GB. Even at the largest file size, you can still fit several thousand photos on one card. I take a ton of photos when on vacation, and recently went on an 11-day trip to San Francisco, Yosemite, and the California coast. I came back with nearly 2,000 photos, and didn't even fill up 2/3 of one 16GB card. I have an extra as a backup (the same way I do with batteries--just in case), but unless you take more than 3,000--3,500 photos before downloading them, you'll never need more than 16GB worth of capacity.
The Manual gives two examples concerning the number of shots per card--8GB and 32GB. At the highest resolution, 1,379 images can be shot using 8GB, and 5,568 images using 32GB. I'm using a SanDisk Ultra SDHC 16GB card myself. FYI, movie recording time at highest quality is 29 min. 39 sec. for 8GB, 1 hr. 59 min. 43 sec. for 32GB.
from the documentation on the Canon web site i can find no limitations on the size of the SD card I have attached the link to the specs page for you further reading. http://www.usa.canon.com/cusa/consumer/products/cameras/digital_cameras/powershot_sx50_hs#Specifications
The new SDXC cards are going to be the maximum size cards of the future once the technology catches up. Right now they are pretty expensive , a SanDisk Extreme 64 GB SDXC Class 10 memory card lists at about $200, but is on sale on Amazon right now for about $70. A SanDisk Extreme 32 GB SDHC Class 10 would have a list price of about $80, but are currently on sale on Amazon for about $25 apiece. Two of them could be bought for less than $50 total.
SD cards are limited to 2 GB. SDHC cards are limited to 32 GB. SDXC cards are for capacities above 32 GB.
It is my understanding that eventually the SDXC cards may even be able to hold as much as 1 TB capacity, but the technology is not yet available to do that. Not counting off-brands like Lexar, the largest capacity SanDisk card offered, I believe is a SanDisk Extreme flash memory card - 128 GB - SDXC. It lists for about $300, but is currently on sale on Amazon for just under $150.