A weak theory could have both reality and mathematically simple structures as its models, from the point of view of an informal metatheory that allows talking about reality (and motivates the theory). A familiar structure (as a “model”) can be used both to study a complicated formal system (natural numbers for PA with its other nonstandard models), and a vaguely defined reality (classical mechanics for the real world with its black holes and quantum mechanics).
A weak theory could have both reality and mathematically simple structures as its models, from the point of view of an informal metatheory that allows talking about reality (and motivates the theory). A familiar structure (as a “model”) can be used both to study a complicated formal system (natural numbers for PA with its other nonstandard models), and a vaguely defined reality (classical mechanics for the real world with its black holes and quantum mechanics).