The term "Occam's razor" first appeared in 1852 in the works of Sir William Hamilton.
I would say that "support to" is used to mean a literal support such as to hold up a roof. He added a steel brace to give more support to the roof. I would say "support for" to indicate approval for...
Give moral or psychological courage..
Technically child support is for ALL the needs for the child, except medical.
You can use either of the terms:Logistics support or logistical support