I saw your note yesterday morning and drafted a reply but was unable to post it. It looks like it still may help, so here it is:
Hello, and welcome to the forum, fishstix
I see the extrapolation you are trying to make: you currently live in the US and cross the border frequently for temporary visits; under your proposed scenario you'd continue to cross the border frequently, sleep in Canada each night in your boyfriend's home (essentially moving to Canada) and cross the border to work M-F in the US. In both cases, you would be entering and leaving Canada at least once a week.
Let's explore each scenario a bit more.
Under your current arrangement, when you cross the border for the day, whether to visit friends or go shopping or just picnic in a park, etc. your visit to Canada is temporary in nature and it is clear that you are living in the US. This means that you have closer ties to the US: your home is in the US, your belongings are in the US, etc. Similarly, if you were to go on vacation for a week, a month or even a bit longer to Canada, if someone looked at the details if your case, it would be clear that you were still be living in the US (i.e., you would be staying in temporary accommodations, have limited goods with you, and many other little things that would add up to living in the US and visiting Canada).
When you propose to go live with your boyfriend in Canada in a marriage-like relationship (necessary for common-law status) you'd be moving your primary residence up to Canada. You'd be sleeping in Canada, your social and financial life would move up to Canada, and you would end up with many/most of your belongings North of the border.
This shift in your primary residence is key.
In order to move to Canada (vs visit Canada), you need to have permission to live in Canada. US Citizens are visa exempt only for temporary resident purposes (i.e., temporary resident = visitor). Therefore, you would need a work permit, study permit, permanent residency, or other form of visa or permit that would grant you the right to live in Canada (short term or long term). Depending on your profession, and if you would consider switching jobs to one in Canada, you may be able to get a wok permit easily. For example, if your profession is NAFTA eligible, you can get a work permit at the border once you have a job offer. Other opportunities would require your employer to get an LMO so that they can show that Canadians can't fill the job. (Note that the US has equivalent programs if your husband were to decide to seek employment in the US instead).
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Given the additional conversation, let me add don't get discouraged. You can continue visiting each other (as you do now) and dating to get to know each other. If you decide you are ready to get married, as soon as you are married, you can apply to immigrate (him to the US or you to Canada). In the US there is a fiancé(e) visa, but keep in mind that once he applies for PR status he'll need to apply for advanced parole and get it approved before he travels out of the US while his application is pending. Take a look at http://www.uscis.gov/family/family-us-citizens/fiancee-visa/fiancee-visas and https://help.cbp.gov/app/answers/detail/a_id/991/kw/k1%20visa%20travel. Canada doesn't have a fiancée visa, so independently of where you get married, you'd apply straight for PR status once you are married. If you decide you want to be able to move to Canada, he can sponsor you (currently takes ~8 months for US applicants if you apply ‘outland'). You'll be able to visit Canada during the process. Once you are a PR you will have the freedom to live in the country you have a Permanent Resident status in.