Luggage may be weighed at check in, but only for the purpose of detecting and hence charging for, overweight bags.
The accumulated weight of the bags at check in is not the figure used for weight and balance.
A standard figure per bag (25lbs under FAA regs) is what is used. On the not unreasonable understanding that some will be under and some over the set weight.
Pax are averaged at 180lbs in summer and five more in winter, once again under FAA regs. Which to be honest seems pretty low given some of the people one sees on the street.
Now add the hand luggage and bear in mind that at least one airline has no limit to weight as long as you can lift it, and it doesn't appear dangerous.
The above figures are as stood the last time I had to know, they may have changed.