For work that don't require any physical strain, my personal experience with overweight people is that their alleged poor performance at work is entirely a prejudice. One can be eager to portrait overweight people as lazy, and may have a hard time going over preconceptions to focus on the actual value of the employee.
some items such as general health are definitely worse in overweight people, which might result in more time off. Others are more controversial - some studies show that being overweight affects brain function
If these are factors, they are very, very marginal. Anyway, in many locations, medical care and medical vacation is not to the employer's charge.
to what extent are any of these answers affected by the type of work being done?
On jobs that even require physical labor, they can be just as efficient.
Some jobs specifically however, such as the military or firefighters, have strict requirements that applicants are athletic and fit, and have sports tests that overweight people would have difficulty with.
So I think for the vast majority of jobs, it makes little to no difference, justifying it should be disregarded and not considered as a factor.
Since you asked for scientifically sources though, a specific study about presenteeism in manufacturing employees concludes overweight workers "experienced a 4.2% health-related loss in productivity" specifically due to "time needed to complete tasks and ability to perform physical job demands." (As Kate points out, mind this is an average, some overweight workers could perform better than the physically fit average)
Other studies are focused on impact of overweight as a whole, and account medical costs and absenteeism as productivity loss as well.
I could not find however evidence overweight people perform any better or worse for non-physical tasks. I would imagine it being especially difficult to measure.