Originally Posted by SDGANDER
....- old tyre side walls are too bad to read any markings.
Since you mentioned 165/13, I can tell you that a 165/13 8ply rating can carry a max load of 1477lbs @ 65psi for a single and 1385lbs @ 65psi for a twin.
It is in order for a car to have different sized wheels providing they are on the same axle. I've no idea about a trailer though.
OK, some general rules. If a rim is too narrow for the tyre it makes the handling a bit floppy and it wears out the centre of the tread. If the rim is too wide, it wears out the edges of the tread but generally the tyre is more stable. The centre of the rim should be inline with the centre of the bearings, however a reasonable displacement is not usually a problem. An offset large enough to put the centre of the rim outside of the bearings is undesirable.