First, let's try to see things from his point of view. Being a man, he naturally feels the need to provide for his partner and later on his family. Not only does he want to provide, he would really like to provide comfortably. So immediately right off the bat, if the girl's family is richer and probably more successful than he and his family are, he will definitely worry for practical reasons.
The insecurities that he feels will be on so many differing levels. Initially, he will feel that he might not be competent enough to be able to support the lifestyle she is used to, let alone pamper and spoil them, given how expensive everything is these days, and prices and standard of living will only continue rising.
With this worry, comes the worry of the different societal class or caste system. However hard we try to deny that everyone is equal these days, there still exists a certain 'differences in class' in our modern day society. Her aunties and uncles may/may not give both her and her partner a slightly hard time with questions like "What does he do? How much does he earn? What kind of family background does he have?" For a guy who comes from a more than modest and humble family, those questions would be kind of uncomfortable, even if they might have the best of intentions while asking him. When her family and extended family gets involved, things might get a little more trickier. They might even go as far as to compare him to her richer, possibly more successful exes, or even "better suitors". These kinds of comments will only make him feel more and more unsuitable and incompetent for her.
So, if we were the man and you were the woman in this scenario, how do we think we should move forward? Well, first of all, the woman has a major role to play in all of this. Her love and the care she shows by telling us not to worry about things like finances will mean the world to us. You can be the voice of reason or the strong pillar to hold us together through seemingly trivial but big things such as family riches. By being practical, grounded and living within each other's means, it will only alleviate any and all of our worries with regards to money.