I ignore trace amounts of sugar, as long as it's less than a gram or two of carbs per serving and I'm minding the serving sizes. If I didn't, I'd be spending more money than I could afford. I eat the $2 wieners with traces of sugar and generic mayonnaise.

I'd caution you, though, against using your weight loss as a method of deciding whether or not those foods are an issue. You're going to lose a pound or two here and there, and it's not going to be linear even if your diet was perfect and exactly the same every single day.