If you are using the same shared parameter for all the weights, you should be able to create some kind of multicategory schedule sorted by category. You'd need to figure out what filters make the most sense to just include those objects as well.

Yes it can make grand summaries.
In the Schedule you can modify either the "sorting" to calculate totals, and also itemize each instance (or not) and how to seperate the fields also (header/footer)
Also in the "formatting" tab of the Schedule you can tell it to calculate totals for a specific value (that are not necessarily in your sorting fields) and it can calculate totals, minimums, maximums etc... Sorry for the image I only have a french version installed but the tabs and buttons are all in the same place on your interface.

I can also add a conditional statement in the formatting tab, I can say
- if value > 100 then make column red (for example)
Then I will see immediately any items that have exceeded my conditional value highlighted in red in the totals column.

I'm not sure if you understood my question, or maybe I didn't understand your answer. What I want is to Add all the Grand Totals together, not how do calculate grand totals. For example, I want (Grand Total 1 + Grand Total 2 + Grand Total 3) = Sum of Grand Totals

no it is not possible.

In a single category schedule it is not possible, Chris' answer above is your best bet, or export to excel and do it there.