Is it ethical for schools to offer merit scholarships, when these are more difficult for students from some socioeconomic backgrounds to get? To illustrate - students with low income perform worse relative to their more privileged peers, and when a low income student is trying to get an education, she has to foot a far larger bill (she doesn't earn the merit scholarships).

If you just look at the amount of rich kids that get full rides because they're good at school, it undermines the merit argument. The current model seems to work again to the idea of social mobility, which we take for granted, by burdening poor people with more student debt. 

Is this assessment correct and if so, is it a justifiable educational model?
Schools don't charge more to low performing students, they provide opportunities to attract and retain high performing students, through merit-based scholarships and grants. While it is probably true that low-SES individuals are less likely to qualify for such awards, it is not fair to surmise that schools are 'charging more' to low-SES individuals.  There are many 'rich' students paying the same tuition as their less-well-off peers.  

The more pertinent question is whether there exist sufficient non-merit based scholarships for disadvantaged populations, and need-based financial aid, to give low-SES individuals opportunity (probably not).