Engineering high biomass plants that produce oil (triacylglycerol or TAG) in vegetative rather than seed‐related tissues could help meet our growing demand for plant oil. Several studies have already demonstrated the potential of this approach by creating transgenic crop and model plants that accumulate TAG in their leaves and stems. However, TAG synthesis may compete with other important carbon and energy reserves, including carbohydrate production, and thereby limit plant growth. The aims of this study were thus: first, to investigate the effect of TAG accumulation on growth and development of previously generated high leaf oil tobacco plants; and second, to increase plant growth and/or oil yields by further altering carbon fixation and partitioning. This study showed that TAG accumulation varied with leaf and plant developmental stage, affected leaf carbon and nitrogen partitioning and reduced the relative growth rate and final biomass of high leaf oil plants. To overcome these growth limitations, four genes related to carbon fixation (encoding CBB cycle enzymes SBPase and chloroplast‐targeted FBPase) or carbon partitioning (encoding sucrose biosynthetic enzyme cytosolic FBPase and lipid‐related transcription factor DOF4) were overexpressed in high leaf oil plants. In glasshouse conditions, all four constructs increased early growth without affecting TAG accumulation while chloroplast‐targeted FBPase and DOF4 also increased final biomass and oil yields. These results highlight the reliance of plant growth on carbon partitioning, in addition to carbon supply, and will guide future attempts to improve biomass and TAG accumulation in transgenic leaf oil crops.