Boyfriend (24 M) is asking me (25 F) to contribute to his rent even though I don?t live at the apartment...

Edit: *Boyfriend cannot stay over my place because I live at home and my mom has expressed that she doesn?t feel comfortable with him staying over. *
Edit: * I do not stay over 3 nights a week every week. I want to clarify that. I am gone for about 1-2 weeks of the month. *
To preface, when I am home, I stay over my boyfriends apartment 3 nights on average. Occasionally the number has been 4 nights but this is very rare. I often stay at my aunts for a week or two during the month to see my supportive medical team because I have MS, so I am usually gone for a full week or two (sometimes more) during any given month.
When I?m home, I only stay the night, and I?m gone by the morning. I bring my own food, and I don?t shower while I?m there. I?ve even pitched in to clean the place while I?m there. My boyfriend is always the one who initiates me coming over, and In the past he?s mentioned how he wishes I would actually spend more time with him.
So my boyfriend?s roommate is the one who started this conversation by texting my boyfriend and asking him to tell me to pitch in with the rent by paying utilities. My boyfriend said he also thinks it?s only fair if I?m there for half the nights of the week, and he thinks I should pitch in about a quarter of the utility bill. (With everything it comes to $400 and he wants me to pay $100 a month).
He knows this puts me in a tough spot considering he makes 3x more money than i do. I am a grad student and I have a chronic illness that limits my capacity to work. That being said, I honestly would like to get other opinions on whether or not I should financially contribute given all the above information. I want to see the best in my boyfriend, but this situation makes me feel uncomfortable.
Tl;DR: I stay over my boyfriends apartment about 3 nights a week when I?m home. upon his invitation. I am away for 1-2 weeks out of the month. I always leave by the morning and I don?t use their utilities /water / I bring my own food. My Boyfriend knows I am financially struggling, but he just asked me to pay a quarter of the utility bill per month ($100 dollars). I would like opinions on whether or not financially contributing is fair


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