I just finished a swap where I shipped to Canada from the US for the first time. I used a regular Manila envelope and sent a hoop, so it was quite light.
My options for shipping were about $6 with no delivery time frame or $20 for a 6-10 day delivery time frame.
I went with the more expensive option because I didn't want my partner to have to wait forever and because I was worried the cheap option wouldn't fulfill the swap requirements.
That's all I know, hope it helps!