Visit - help/advice needed

My Mexican boyfriend is coming to visit me this summer for two weeks. Right now, he is not intending to get a visa and come as a short stay (up to 90 days; he'll only be here 2 weeks). That dictates that he must be able to leave the country after those two weeks (he'll have a return-ticket, and also he attends university back at home, so he'll have a letter from them), but also it says must not have recourse to public funds.

I'm on incapacity benefit, living with my mother (who works) in council-rented accomadation. My mother is in full-time education and, as such, doesn't pay council tax.

Am I right in thinking that because of this they might not let him into the country? And does it mean that he couldn't stay with me and my mother those two weeks? If he couldn't stay with me and I booked us into a hotel, would that also not be allowed because it would have come out of my IB?

He's going to have about £150 with him when he travels, but will they look at my income as IB and say no you can't come into the country?

Also, I'm planning to help pay half of the ticket-cost for him, but that would be out of IB (about £350; I have some savings but they came from IB too.) Would they look at this and not let him into the country?

Or should he be getting a visa?

This is all so confusing. I've been having endless sleepless nights about this. I just don't want him to come here and then they refuse him entry and send him back to Mexico the next day, yet I really want to see him as I miss him a lot. Can anyone help me before I go insane?