The "mer" refers to the number of residues in the peptide. A peptide with 10 amino acid residues with be called either a decapeptide or 10-mer peptide. It does not indicate the Mr or MW of the peptide, although you can estimate the Mr using 100 as an average residue Mr. The "mer" nomenclature is also used for other polymers indicating the number of residues in the polymer.
The term "mer" comes from the Greek word "meros" which means part. A residue can be a part of a polymer, but so can a sub-unit or monomeric unit be a part of for example, a tetrameric protein.. In biology/biochemistry the terms, dimer, trimer, tetramer ect are used for larger biomolecules associated in a quaternary conformation. If the length of an polymer or oligomer is described in terms of unique residues, there is a number before "-mer", such as 21-mer for a 21-residue peptide. The 21-mer peptide can exist for example as an monomer or a dimer in solution. Petide leng up to 50 residues as described with -mer notation, while the number of amino acid residues are noted for proteins, rather that using the -mer notation. For DNA and RNA, codon/anticodon would be a 3-mer, but that is seldom used and the terms triplet or kodon/anticodon have been adapted. We do use mer for the length description of longer sections of RNA and ssDNA, but number of base pares are used tho describe the length of dsDNA.
Mer means the number of residues/amino acids in a protein. In a similar manner, Mer may also be involved in some types of compositional information of a protein to extract, like 2-mer (dipeptide) composition, 3-mer (tripeptide) composition to k-mer (k-peptide) composition.
I agree with Maria Rautenbach. Mer is usually used for the peptides and a 19-mer peptide means a peptide that might have 19 amino acids or 19 residues. Each residue might be included in more than 1 amino acid.