"giant food stores circular for this week" is a common search among shoppers in the United States looking to plan their regular shopping around current pricing and promotions. For Giant, specials and promotions are generally published on a weekly cycle, so checking the most recent catalogue is more reliable than relying on results that may reference an older promotional period.
Comparing multiple retailers rather than committing to one by default tends to produce better value for a typical shopping list, since promotional depth and timing genuinely differ retailer to retailer even within the same country.
The full catalogue directory for the United States brings together current offers from multiple retailers in one place.