Need advice, what formula to use for homicide research

I'm trying to arrive at homicide rates for different regions. I have each country, their population, and their violent death rate. However, each country's contribution to the total needs to be weighted based on how large their population is. (see image attachment)

For example, if you combine Belgium (1.5 homicide rate, 10,827,519 population) and the United States (6.1 homicide rate, 310,225,000 population):

I take the total 321,052,519

Then if I divide the larger US pop by it, I get 96.6%
and Belgium around 3.4%

So how do I then figure out what the total between the two would be, if the homicide rate is to be weighted by each country's population? I'm guestimating it would be around 5.9 in this case.

In the case of Africa I have almost 30 countries I need to properly weigh in order to arrive at an African Homicide Rate. So I'm trying to figure out a good multi-step formula to pull it off.

Does anyone have any ideas? Or can they point me to a tutorial on how to do complex, though common problems like this?

Thanks much.