How do we build a deck/balcony over our back patio?

You would need separate footers for the posts. The patio isn't made to carry the weight. The patio could be cut where the posts would go and footers dug and filled in with concrete.

Do some leg work first and start at the city planning office. Find out what's needed and who's typically responsible for the permits in your area. Look at decks and decide on what's right for you and plan a budget. Ask around for reliable contractors. Cutting into an upstairs portion of your house and building a load bearing deck is not a DIY project unless you are very familiar with home construction. Good luck.

You may also consider a cantilever balcony. Would require less posts.

Hello! It is definitely possible, but it would be best to obtain professional advice to ensure the work is up to code and meets standards. This is important, especially when you attempt to sell your home in the future. You would not want a home inspector to indicate to the buyer that the work was not properly done or is not up to code. The link below can at least get you started and give you some things to consider if you are attempting to tackle this project yourself. Good luck!

Start by getting a permit, and when your done, the building inspector will be out to see if it's up to code. Unless your a carpenter, I'd have this done by a professional. You want this to look good, and most of all safe.

No, you shouldn't put the posts on the patio. Posts need to be several feet below the surface and below the frost line. I really appreciate the high quality instruction provided by the YouTuber called Essential Craftsman. Search his videos https://www.youtube.com/channel/UCzr30osBdTmuFUS8IfXtXmg