In general, store policies are motivated by two main things: 1) cost efficiencies and profit, and 2) customer preference.
Just as with any other business, grocery stores need to be profitable to stay afloat, so they continually look for ways to save money. Plastic bags are surely a detriment to the environment, and grocery chains know this, but they are much, much cheaper for them to use and this increases their profit margin. They are also easier to store (take up less space) than paper, and lighter to ship.
Some customers still want to use paper bags because they are often made from recycled paper (which doesn't consume additional trees) and if they are thrown away, they break down very quickly, compared to plastic especially since it is virtually permanent. Customers who make that choice, however, are willing to pay for those bags, and grocery chains know this as well, so it helps boost their profit margin by charging customers who are willing to pay for paper, and giving plastic bags free of charge to those who won't.
In the end, though, grocery chains and all other businesses will do whatever the customer wants them to do. Organized economic boycotts of businesses that have what you think are objectionable polcies remain the most effective form of protest there is in my opinion.