If you want to express the largest amount of a certain or a few proteins using a plasmid, does it make sense for the antibiotic resistance gene to come after genes for proteins you intend to synthesize? So that the promoter and RBS/origin of replication would specifically come before the proteins intended to be synthesized and the bacterium would put less resources into its antibiotic resistance? But would that be canceled out by bacteria not surviving as much as if the antibiotic resistance gene is downstream of the other proteins? Or is it roughly the same in either order because they're both being synthesized anyway?
The relative placement of genes on a plasmid should not affect their expression.
Both will be expressed and to what extent is dependent on the strength of the promoters and a few other factors like codon availability.
However where you ultimately plan to express these genes can be an important consideration in plasmid design. For example, if you are designing a binary vector for agrobacterium mediated transformation of plants then positioning the plant resistance cassette next to the left border is a sensible move.
Placement can alter protein expression. You could for example make a synthetic operon, and proteins located closer to the promotor will usually be expressed more. You could include your resistance marker in this, and probably get some interesting effects.
However, the resistance marker is usually not such a high metabolic burden that it makes any difference. Increasing expression would be needless. Decreasing expression would free up some resources, but it's extremely likely that your expression is already limited in some other way. Probably promotor strength, plasmid copy number, protein solubility or toxicity.