"the more fortunate should renounce some of their rights"

When talking about rights, Pope Paul VI taught that those who lack rights are to be given preferential treatment. This is true even if those with excess are more heavily burdened:

"...the more fortunate should renounce some of their rights so as to place their goods more generously at the service of others."

Even if this extra burden on those with excess is unfair or unequal:

"Without a renewed education in solidarity, an overemphasis of equality can give rise to an individualism in which each one claims his own rights without wishing to be answerable for the common good."

Now keep this is mind when the Church teaches that we not only have the right to life and liberty, but all human beings also have the right to food, clothing, housing, basic education, health care, employment, and immigration. Individuals who lack access to these basic things are to be given preferential treatment, even if unfairly.

From Octogesima Adveniens:

"In fact, human rights are still too often disregarded, if not scoffed at, or else they receive only formal recognition. In many cases legislation does not keep up with real situations. Legislation is necessary, but it is not sufficient for setting up true relationships of justice and equity. 

In teaching us charity, the Gospel instructs us in the preferential respect due to the poor and the special situation they have in society: the more fortunate should renounce some of their rights so as to place their goods more generously at the service of others. 

If, beyond legal rules, there is really no deeper feeling of respect for and service to others, then even equality before the law can serve as an alibi for flagrant discrimination, continued exploitation and actual contempt. 

Without a renewed education in solidarity, an overemphasis of equality can give rise to an individualism in which each one claims his own rights without wishing to be answerable for the common good."

You can read the document here:

https://www.vatican.va/content/paul-vi/en/apost_letters/documents/hf_p-vi_apl_19710514_octogesima-adveniens.html