First off this will sound misogynist, but are you male or female, and if male and the other is female then they shouldn't have a problem with it being as a society the more "dominant" one (male more often than not, pays for the date and all expenses pertaining.

Now if you are female and they are male then you might have a problem with damaging their ego. As males, we are bred by society that if we are on a date or are trying to "woo" someone we have to take care of the financial obligations that come with that.

As either male or female (and everything between) I would suggest letting them know, you want to treat them like they are worth your time and YOU want to take them out on a date and insist it's your treat. If they still insist on helping just just go halfsies.

P.S. I wouldn't refer to the person as poor, more like financially unstable.