This summary shows more reactions to Moderna vs Pfizer to first dose: fever: 8.2% vs 5.8%, chills 8.4% vs. 5.5%. So yeah, more side effects, but not a huge difference.
https://www.sltrib.com/news/2021/03/26/comparing-covid-vaccines/There was also a specific rash that was reported for Moderna, about a week after injection.
https://www.massgeneral.org/news/press-release/MGH-researchers-call-for-greater-awareness-of-delayed-skin-reactions-after-moderna-covid19-vaccineAlso slightly more allergic responses with Moderna:
Scientists from Massachusetts General Hospital and Brigham and Women's Hospital administered email, text, phone, and smartphone app survey links to 64,900 employees who received a dose of one of the two mRNA coronavirus vaccines from Dec 16, 2020, to Feb 12, 2021.
A total of 25,929 employees (40%) received the Pfizer vaccine, while 38,971 (60%) received the Moderna vaccine. Eighty-one percent returned at least one symptom survey, which were sent each day for 3 days after vaccination.
Among all vaccinated employees, 1,365 (2.10%) reported acute allergic reactions, defined on the survey as itching, rash, hives, swelling, and/or respiratory symptoms.
More Moderna vaccinees (2.20%) reported symptoms than Pfizer vaccinees (1.95%).https://www.cidrap.umn.edu/news-perspective/2021/03/very-few-severe-allergic-reactions-tied-mrna-covid-vaccinesSo, yes, slightly more side effects with Moderna, but not 3 times as much, so not obvious that it would relate to the weight of the vaccine. What contributes to that difference in weight? Is it a difference in the amount of mRNA, or are there differences in the amount of lipid and sugar included in each vaccine? I really don't know the answers to any of these.
But speaking of drawing conclusions from an n of 2: My mother had no reaction at all, while I had a sore arm both times (Pfizer). I had read that side effects decrease with age, so from this I concluded that my mother must be older than me.