I make freezer jam like this, too, but I most often make strawberry and I use frozen berries from the grocery store frozen fruit section: just thaw in fridge then mash and measure. So good!
Normally raspberries are available only now in July, some maybe left in August and that's it. If it is a jam, or any kind of processed product, sligthly damaged berries are fine. They usually have some dry sections. Garden berries may have maggots inside, particularly late in the harvest. This supermarket fruit is so perfect as if it came from god in the sky. Would make less mess and dirty tools if you weighed the berries and put the plain sugar into the bowl. Then use a funnel to fill those smaller jars. It looks liquid enough for a small diameter funnel. I like to crush apples and put in the freezer. They don't separate unlike watery berries. But so much stuff goes into the freezer that is always full.
I just made fresh raspberry jam but I used 8 cups of fresh berries and mashed them down to 5 cups, added 3 cups of sugar, 2 tables spoons of lemon juice and 1 box of reduced sugar pectin. I brought it to a boil for only 1 minute - and my jam is plenty sweet and it jelled up really nice. I can't imagine using 5 1/2 cups of sugar, that sounds like diabetes in a bottle. No offense, really, but the jam I just made is sooo amazing and it's half the sugar and more fruit!! Add lemon juice it makes all the difference.
Thx for your recipe however,I find this is too much sugar for my liking. Tip: I use chia seeds as gelatine to make my raspberry jam and monkfruit sugar. 👍🏼😃