I disagree with the above post, because tobacco is always in demand, and has consistently been so over time (it helps that your customer base is largely addicted). So the key to the focus of the tax burden - on customer or seller, is the degree of competition in a local market. Are you the only smoke shop or store in town? Then you can pass on the entire tax burden to the consumer, because you have a de facto local monopoly. The more local competition there is, the more likely the seller is going to absorb some or all of the tax burden as it increases. This is also because tobacco is very rarely the only product sold in these stores, and as they can count on tobacco buyers to show up consistently, it may still be profitable to make very little or nothing on the cigarettes if you get them into your store to by high profit items like pop, sundries, lighters, food etc.
How the tobacco "sin" tax is shared between buyers and sellers:
I assume that we are talking of the tax burden that is placed directly on tobacco, as stated in the question, and not taxes that are placed on the property or income of the retailer. The taxes that are placed directly on tobacco are placed at the place of manufacture (excise taxes) and the place of sale (sales taxes).
I can't imagine that the tax burden on tobacco would ever be shared between the buyers and sellers, because the seller must pass on all of his costs to the buyer or go out of business. Thus the buyer would always carry the entire burden, would he not? It seems so to me.
To answer this really precisely, you would need to know a fair amount about the supply and demand of tobacco. The most important thing to know would be how elastic the demand for the product is.
The more inelastic the demand for a product is, the more that the tax burden can be shifted completely to the buyers. If people will buy tobacco regardless of the price, sellers will simply pass on all of the tax burden.
You might also need to think about the amount of competition and the profit margins of the industry. If profit margins are already at a minimum, all new taxes will have to be passed on to the customer.