Tricky, but I think that your best bet centers around providing alternative foods (which I know you've already done), explaining why you would prefer not to order food, and explaining that you don't feel comfortable being treated all the time. Basically, exactly what you've expressed here. This breaks down along some fairly clear lines for me.
- You are up against a hard constraint regarding these meals.
These meals may or may not be expensive in absolute terms, but ordering prepared food from a restaurant is one of the most expensive ways to eat. Even if you can make your budget work to include such meals, it may still be an undesirable way to spend your money. I think that most people can understand this, and it sounds like your issue with your friends is that they don't understand that this is an ongoing situation for you.
It's not that you would have a hard time with the cost of pizza this week (prompting the "our treat, you'll get us next time" argument), it's that the pizza is too expensive in general. This seems like the key point your friends are not acknowledging-- alternating who pays for food doesn't change what you spend, it just distributes your spending differently over time.
For this one, I only see a couple of choices. You can specifically budget for the takeout with your friends (which would mean scrupulously not ordering food at other times if your budget doesn't allow for that), if that is affordable and desirable. Otherwise, telling your friends clearly that you can't afford such frequent takeout. That leads to number two:
- Your friends are more comfortable treating you than you are being regularly treated.
Based on what you wrote, it seems that your friends enjoy your company and don't really mind paying for your meals in order to have the specific meals they want. It's not clear to me if this pattern is well understood on their end-- are they explicitly OK paying for your meals most of the time?
If not, this weekly contention may be hiding that pattern and cause ill will down the line. Even if they don't mind it, it seems that you do, in which case they should be respectful of your wishes. But that also means that the takeout will be off the table, so to speak, when you spend time together. Of course, takeout isn't the only food available, which brings us to three:
- Your friends consistently decline other food options, seemingly regardless of circumstance.
Your friends appear to have a preference for takeout. Some people do; when I spend time with friends, it is often easier and "more fun" to order food. I'm not opposed to cooking, but may not want to go to the trouble. I also don't want to mooch off of others' cooking without contributing myself, so I'm stuck cooking or pushing for takeout. Your case may be similar. In the same way that you don't want to be paid for all the time, they may not want to cook, or not cook and then eat what you've provided all the time.
Whatever the reason, their preferences on alternative meals is forcing you into either paying more than you're comfortable with, or forcing everyone to go hungry for the night. If these are your friends, I doubt that either of these is what they want to happen. I don't know them or their minds, but what seems most likely to me by far is that they don't fully appreciate the situation they are putting you in. They might be more open to alternatives if the did have all the information.
I think that this is less an issue of being polite than of being clear and direct. Efforts at politeness have produced individual, discrete instances where they address your polite cover rather than your actual situation. If they knew that you can't order food weekly (or are just not comfortable with doing so) rather than over a string of "just this one time"s, they might press you less on ordering. They are much more likely to understand your situation if you just tell them, something like "I'm trying to be extra careful with my money for now, and it's a real challenge to do this every week. I'm not sure I can keep it up".
Even that has a fair amount of hedging in it. If you are really concerned about telling them flat-out, a more proactive message may work. If, for example, the weekly hangout incorporated everyone making a meal together you could avoid the cost of the takeout (and maybe save even more by buying sale items in large quantities!). Some of my friends and I do this, though irregularly. But I have to assume that they prefer your company to takeout food, and would be willing to do things differently if they really understand that this is a significant hardship for you.