Object-oriented theories have previously been used to reveal how the global climate and other entities became discrete, malleable, and salient objects of contestation and governance. However, there has been a failure to theorise different kinds of governance-objects that have fundamentally different characteristics and political implications. This article contributes both to object-oriented theory and to climate change literature by suggesting a distinction between ‘weak’ and ‘strong’ governance-objects, arguing the former are distinct but malleable only in terms of (not) perturbing them. This implies a ‘natural’ or baseline state that governance aims to minimise movement from. ‘Strong’ governance-objects are more radically disembedded and malleable, their purpose or telos not tethered to a pre-given baseline. This weak/strong distinction is developed and used to understand implications for international climate politics of emerging techniques to deliberately modify the climate often grouped as ‘geoengineering’. The growing reliance on large-scale carbon removal and potentially on solar radiation modification techniques has the potential to shift climate from ‘weak’ to ‘strong’ governance object, dis-embedding it not only from carbon emissions and concentrations, but also untethering climate governance from the aim of staying close to a pre-industrial state. This potentially politicizes the climate in new ways, while also allowing a more reductive climate politics of global average temperature, or even one dominated by economic goals such as growth. Weak and strong governance objects have deep implications for the politics of climate change and the international system.