The financial objective, when sizing a Battery Energy Storage System (BESS) for installation in a microgrid, is to maximise the difference between discounted BESS benefits and discounted BESS costs. This may be described as maximising Annual Worth (AW). However, one drawback of sizing microgrid BESS using AW is that the scale of investment is not taken into consideration. This can lead to unrealistic BESS sizes. This paper presents two multi-objective optimisation (MOO) models to account for the scale of investment required in sizing BESS. The first model, Paired Comparison, utilises two objective functions: Daily Worth (DW), which maximises daily benefit cost differences a BESS installation provides a microgrid; and Daily Cost (DC), which minimises the daily cost of a BESS installation. The second model, called Rating Method, uses the objective functions DW and Daily Benefit-Cost Ratio (DBCR), the latter of which maximises the relative measure of BESS benefit and BESS cost. Both models are solved for a test microgrid system under three different scenarios using Compromise Programming (CP). For system designers who rank objective functions by importance, the Rating Method is the appropriate approach, whereas system designers who rank objective functions by absolute values should use Paired Comparison.