OP--do you have a current script for an Epi-Pen? Just as an FYI, if your script is not current and your Epi-Pen is expired or isn't labeled with your prescription label, the EMT's and Paramedics can not use it on you. If EMT's respond, they DO NOT carry Epi-Pens or anything but O2. Some paramedics carry epiniphrine, but not all.
I just weighed mine on my little digital kitchen scale, it weighs 2.2 ounces. (OK so I'm bored tonight). For something as lifesaving as an Epi-Pen, I don't think there's really a good reason not to carry one.
There are nurses (can't administer medication), EMT's and Paramedics in the parks, but it can take up to five minutes for them to respond, and that's too long to wait if you are having an anaphylactic reaction. That in itself is a good reason to carry it. It's kind of like life insurance, you hope you never need it, but you're very glad you have it if you do.
Anne