I appreciate your predicament; you both want to make a change, but your girlfriend isn't ready to do the work.
You can tell her, these supplements don't work, and I have a few reasons to back that up:
1) ALL weight loss supplements come with a suggested diet and weight loss plan to accompany taking the pills. ALL weight loss supplement ads and commercials have a little asterisk * that states "results not typical". Taking an over-the-counter pill alone will NOT cause weight loss.
2) If your girlfriend does not eat less AND exercise more there is no way she will lose weight. It's a simple equation: Calories OUT must exceed calories IN in order for their to be a net energy loss, which results in weight loss.
3) Whenever skeptical/hopeful that a supplement works, I use Oprah as my guide: Is Oprah still overweight? YEP. She has a slew of employees and investigators scouring the world for the secret weight loss potion (Is it Optifast? Is it Garcinia Cambogia?) If there is ANYTHING out there that promotes weight loss, Oprah's staff will have discovered it and Oprah will be nice and skinny. Until I see a skinny Oprah, I know there are no magic weight loss pills available
The bottom line is, your girlfriend may choose EITHER to eat what she likes OR to lose weight. You can't have both. Not every day. That would be like saying "I want to save for my retirement but I must buy these new shoes/new purse/new iphone/new car in the meantime". Pick one; you can't do both. But you can buy a pair of shoes once in a while.
She doesn't have to give up pizza and pop forever, but here's a simple equation: Eat 100 fewer calories a day and lose 1 pound a month (approximately). Give up 3 sodas a day (which it sounds like she has) and lose about 3 pounds a month.
Can she compromise and eat relatively healthy for ONE day a week? Perhaps she can gradually up the number of days per week that she eats in her target calorie range.
Or: If 1300 calories leaves her too hungry, try going up to 1500 per day for an easier day and just a tad slower weight loss.
Burning 100 calories works the same: Burn 300 calories at the gym each day, lose 3 pounds at the end of the month; burn 300 calories 3 days a week, lose 1 pound per month.
She doesn't 'need' to eat frequently and more and junk food, she just WANTS to. Everyone has to put up with a little discomfort when they are making a change--every change is difficult and takes thought and mental energy.
She might try coming up with a list of the reasons she wants to lose weight to find her motivation. At this point the in-the-moment motivation to eat what she feels like is outweighing the desire to lose weight.
One weight loss plan I highly recommend (and lead teleclasses with) is The Beck Diet Solution.
Either way, when she's ready to lose weight she'll have to be ready to do the work.