The US and multinational corporations have benefitted on the backs of Mexicans...and not just on their backs, but by completely exploitative methods of making money from Mexican people and Mexican resources: from trade agreements which do little for Mexican working people, especially in agriculture, and much for the US, from unfair trade practices which undermine the internal Mexican agricultural economy, from industrial practices both in manufacturing machines and cars, etc, and animals which pollute Mexican air, land and water and which not only kill Mexican jobs but break up Mexican families and society by forcing internal as well as external migration for the few new jobs they offer which certainly don't compensate as such jobs do in the US, for failing to contribute to Mexican society and education, etc. etc.
If the US didn't pretend it was anything but a greedy empire, one could bemoan the situation without expecting redress, but the US pretends it is fair and just and democratic. It owes Mexico reparations.
Much of the southwest US also WAS Mexico, and many people there of Mexican and Spanish heritage were there a long time before any Anglos were. They have ties across the border which have grown with time. Mexicans who have migrated legally more recently also have ties across the border.
Undocumented Mexicans as has been said frequently come to do jobs that are available to them and not generally wanted by others. This is also an exploitative situation, doubly so because it is so very hard to get one of the very limited legal visas for blue collar and agricultural work in the US.
I can't speak for Mexicans, but I suspect that many stay because of the difficulty of going to and from home. Many find themselves with second families...and why wouldn't they? IT is hard to find yourself in a foreign environment without social ties. I don't suspect that they have the dream of American citizenship Americans think they have: that is, with fair treatment including the right to working people's benefits and the ability to go back and forth across La Frontera, most probably wouldn't seek citizenship. Working people's benefits would also legitimize their presence and give them credit for taxes paid ... which many now pay even as illegals.
Aid should be given to Mexico NOT to make it a fertile place for US investment but to help Mexico in a way that keeps things Mexican. Aid maybe should be thought of as reparations.