$12 bi-weekly is $312/yr, not that significant. Now if you meant twice weekly, that's $1,248; that's a good bit of money (maybe enough to justify a heated discussion), but I'd be more concerned about the fact that both grocery bills are excessive at that point.

How many times has he checked how much she's "wasting?" Store prices fluctuate frequently, perhaps he'd find that the next two trips were indeed cheaper at Kroger's. Is Meijer out of the way while Kroger is more convenient? Has he sat down to calculate the savings Kroger may be giving in terms of fuel, car wear, and his wife's time?

If he's stressing out this much over the grocery bill (I can't judge, been there myself), I think they need a budget. Set a grocery budget, and don't complain if spending stays within budget. Seriously, if the budget is $140 and she spends $135, don't worry if the same groceries would have cost $125 elsewhere. Give both some spending money that can be spent however whyever; if the grocery budget is $140 and she spends $150 with $10 of that coming out of her misc money...leave it be. If she'd rather forego $10 worth of new shoes than switch stores...she's still saving $10, so consider it a small victory.