It will be slightly larger than the Me-Me gauche interaction, but extending a straight alkyl chain like that (i.e., from Me to Et to n-Pr, etc.) has a very small effect on the strain because the floppy part of the sidechain can situate itself pointing away from the gauche interaction. If you were to look at a Me-Me gauche interaction, most of the conflict comes from 2 of the 3 H atoms on the Me group (the third H points the other way), so substituting the third H with an Me is a small change in the actual interaction.
If the groups were locked into close proximity, there would be a large effect, as your intuition suggested. You can see this in what is called a "syn-pentane" interaction. The syn-pentane interaction is responisible for the strain in one of the chair flip conformations of cis-1,3-dimethylcyclohexane. In a cyclohexane system, these interactions are usually called 1,3-diaxial interactions, the syn-pentane terminology usually refers to an acyclic system.