The OP question as written can't be answered.
As has been said, who are 'the rich' and 'the poor'? Also, what does 'to pay for' mean? Most of 'the poor' pay for themselves on a day to day basis - they just don't have much left over. If there are cases where someone working a full week needs to be 'paid for' by others then we need to adjust minimum wage levels upwards. Not to do so means both that the State is subsidising employers and that workers are being exploited. It's a double whammy if that employer is also avoiding (or evading) paying tax.
Where people of almost all income groups might need subsidy is in times of crisis, such as when they are ill. If someone needs a transplant, or a long course of expensive treatment, it could quickly add up to more than they had contributed in terms of tax, so they are, effectively, being 'paid for', whether they are 'rich' or 'poor'. I have absolutely no problem with that, and don't suppose many people in the UK do.
Averages will mean that on the whole it is not 'the rich' who subsidise others - it will be middle earners as there are more of them. Plus, as has been said, those who can afford accountants and IFAs are more able to find ways to minimise tax, which are not available to 'the poor'.
I think that one way to reduce resentment would be to increase the number of universal benefits, so that everyone gets a bus pass, child benefit, free health and social care etc, and at the same time bring in universal taxation for all who are able to work, so there is less outright and obvious subsidy of one group by another. That way it wouldn't be the case that those who work and pay income tax feel that they subsidise those who don't choose to do so, everyone is covered for basic services such as health, education, defence, law and order and so on, and if the tax system is organised so that those who have more pay more (eg tax on unearned income as well as wages and salaries) then it's fair. Everyone is provided for, and those who earn more are still better off after that is assured.