The short answer
The state you are buying in sets the amount, and the store applies that state's figure at the counter. Federal law sets no figure of its own for a lawful sale. What it does is prohibit distributing a controlled substance except where federal drug law authorizes it (21 U.S.C. § 841. Prohibited acts A). The page for the state you are buying in carries the figure, written the way that state writes it, with the law it comes from, or says that the state sets none.
The detail
A purchase limit is a cap a state sets in its own cannabis rules, and most states that license a cannabis store set one. A few set none at all. Where that happens the state page says so, and says what the state limits instead.
A state's cap governs what the store may sell. Federal law reaches what you then hold, and possessing a controlled substance is a federal offense unless federal law itself authorizes it (21 U.S.C. § 844. Penalties for simple possession). A state's purchase limit is not among the exceptions that section writes. What federal law says about weed sets out what federal law does with a license a state issued.
A state writes its cap per transaction, per day, over a set number of days, as a supply covering a set number of days, or as one flat amount with no period at all. Where the cap runs over a period, a purchase you already made counts against it. The state page says which form its own cap takes.
A possession limit and a purchase limit are two separate limits, and a state may set both. The possession limit is the amount you may lawfully have. The purchase limit is the amount a store may sell you. The two match in some states and differ in others.
Where a state licenses both recreational and medical stores, it can set a separate figure for each, and it can write the medical figure over a longer period than the recreational one. Holding a card can change the amount a store may sell you in that state.
A state that licenses recreational stores usually writes its cap by product form, with a separate figure for flower, for concentrate and often for the milligrams of THC in edibles. Where only a medical program runs, one figure more often covers whatever form you buy.
What varies by state
Each figure is set by one state and applies only inside that state. The 43 states and districts that license a cannabis store of either kind each answer this for themselves: Alabama, Alaska, Arizona, Arkansas, California, Colorado, Connecticut, Delaware, District of Columbia, Florida, Georgia, Hawaii, Illinois, Iowa, Kentucky, Louisiana, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Jersey, New Mexico, New York, North Dakota, Ohio, Oklahoma, Oregon, Pennsylvania, Rhode Island, South Dakota, Texas, Utah, Vermont, Virginia, Washington and West Virginia.
In 5 more the only counter you can lawfully buy cannabis products from sells hemp-derived ones, and no purchase limit for cannabis reaches it: Kansas, South Carolina, Tennessee, Wisconsin and Wyoming. Another 2 license no cannabis store at all: Idaho and North Carolina. This site cannot say for Indiana.
What to watch out for
A state can set the purchase figure below the possession figure, and the store applies the purchase figure.
Where a state lets one product form be counted against another, it writes that conversion into its own rule.
Where to go next
Cannabis law, state by state holds a page for every state and the District of Columbia, and one for federal law. Each state page carries the purchase limit, the possession limit and the minimum age, with the law behind each one, and the date a person last checked them. Where a state's own text could not be read, the page says so instead of guessing.
The store directory searches by city or by ZIP code. Each store page names the authority that licensed the location and what you need in order to buy there, and gives the license number where the state publishes one.