Weekly free meals - good or bad?

I'm not sure what you mean by "free" meals. It sounds like you mean a meal that you do not log, or maybe a meal in which you intentionally exceed your calorie goal.

Ultimately, if you are consistently in a deficit, you will lose weight; if you consistently eat as many calories as you burn, you'll maintain your weight; and if you eat more than you burn, you'll gain. This is true regardless of whether you choose to log your food. Your body doesn't care if you think of a meal as free/cheat/etc.

If you want to stay within your calorie goal yet eat larger meals sometimes, you can follow a weekly calorie goal or "bank" a few calories each day before your larger meal. Many people intentionally eat less during the week so they will have extra calories for the weekend. Your weight will still behave as expected if you are within your weekly calorie goal.

Whenever you eat more or differently than usual, the scale will probably go up a few pounds. This is almost always due to water/weight fluctuation, not fat gain. I'm not sure if that's what you meant by "pay for days." You might have also meant that you feel sick after eating a big meal, in which case...well, I wouldn't advise eating things that make you sick.

A more sensible approach than a 'free' or 'cheat' meal (which often gets translated to 'eat anything and as much as I can') is to either save some calories each day to allow for a higher calorie meal once a week, or just have a maintenance day once a week and accept a slightly slower rate of weight loss (ie, with both of these you are still aware of how many calories you are consuming, and have a limit that doesn't undo your entire calorie deficit for the week).

Mentally, having a meal or a day where you can eat a bit more and fit in foods you may not be able to when at a deficit can be a very good thing. It can be the difference between sticking it out and throwing in the towel for some people. But if you're going so overboard that it's significantly effecting your weight loss efforts, you're doing it wrong.

NB, it's perfectly normal to see a higher scale number for up to a few days following a higher cal day. This tends to be from higher sodium intake (depending on what you ate), more food in your system, and water retention from glycogen replenishment. Concentrate on your overall weight loss trend, rather than day to day fluctuations.