Social security stopped my pay because they said my roommate and I are a couple and were common law married when in fact

The burden is on you to show to SSA that you are your "roommate" are just that and nothing else. You do not tell us what SS disability program you are on; however, I am assuming you are on SSI. SSI has strict income/asset guideline ($2k for single; $3k for married, etc.). SSA also takes the position that free room and board, free meals, etc. are considered income for the purposes of SSI (it is referred to as in-kind income). So if you are not married, your income and assets (including in-kind imputed income) must be under $2k. I have provided a link below that should help you. I would contact SSA or go into your local field office and explain everything. If that does not work then you may need to consult with a SS disability attorney (use the link above to search for an attorney in your area). You can also contact your local/regional legal aid office or the local Bar Association for a legal referral. Best of luck.

You have to show you are not holding out as husband and wife by showing 1) separate bank account; 2) no joint bills or property; 3) separate car title; 4) statements from friends that you are not a couple and do not hold out as such; 5) sleep in separate rooms; 6) pay own share of bills. These are just some examples.

The prior two answers are absolutely correct. You, perhaps with the assistance of counsel, need to prove that you are not holding yourselves out as a couple. Separate tax returns, bank accounts and the like would be one place to start.

I agree with other posters that you need to look into the law for your state relating to common law marriage and show SSA why you do fit within your states definition. I also agree with other comments that this will only relate to whether your roomate's income/resources are deemed to you (counted towards your eligibility), you still could have a reduction in the amount you get each month in SSI due to any assistance your roomate provides.