Could you tell me how the Stabiliser helps to support insulin sensitivity?

Mulberry extract blocks carbs what lowers blood sugar levels and therefore decreases insulin concentration. This improves glucose tolerance of the cells (also in normoglycaemic adults) resulting in a better sensitivity to insulin. https://pubmed.ncbi.nlm.nih.gov/28225835/

Basically, glucose tolerance decreases when there is too much sugar in the bloodstream to protect the cells from a high influx of sugar. The sensitivity of the cells to insulin is lowered as our body reacts with an overproduction of insulin (insulin resistance as a result to protect the cells that contain too much sugar).

Berberine can increase insulin sensitivity by activating AMPK and inhibiting another enzymes, based on this meta-analysis & systematic review on Berberine.

More scientific references: 

• Birdsall T, Kelly G. Berberine: therapeutic potential of an alkaloid found in several medicinal plants. Alt Med Rev. 1997;2(2):94-103.
• Lee YS, Kim WS, Kim KH, et al. Berberine, a natural plant product, activates AMP-activated protein kinase with beneficial metabolic effects in diabetic and insulin-resistant states. Diabetes. 2006;55(8):2256-2264.
• Xu Z, Feng W, Shen Q, Yu N, Yu K, Wang S, Chen Z, Shioda S, Guo Y. Rhizoma Coptidis and Berberine as a Natural Drug to Combat Aging and Aging-Related Diseases via Anti-Oxidation and AMPK Activation. Aging Dis. 2017 Dec 1;8(6):760-777. doi: 10.14336/AD.2016.0620. PMID: 29344415; PMCID: PMC5758350.
• Yin J, Xing H, Ye J. Efficacy of berberine in patients with type 2 diabetes mellitus. Metabolism. 2008 May;57(5):712-7. doi: 10.1016/j.metabol.2008.01.013. PMID: 18442638; PMCID: PMC2410097.

Chromium Picolinate may be effective at improving insulin response. The binding of insulin and the activation of the insulin receptor require the availability of chromium in the form of a low-molecular Cr-binding substance called chromodulin, which has also been called glucose tolerance factor. Insulin resistance and Glucose tolerance are sometimes used for same meanings. 

Scientific references: 

• Talab AT, Abdollahzad H, Nachvak SM, Pasdar Y, Eghtesadi S, Izadi A, Aghdashi MA, Mohammad Hossseini Azar MR, Moradi S, Mehaki B, Moradi S. Effects of Chromium Picolinate Supplementation on Cardiometabolic Biomarkers in Patients with Type 2 Diabetes Mellitus: a Randomized Clinical Trial. Clin Nutr Res. 2020 Apr 24;9(2):97-106. doi: 10.7762/cnr.2020.9.2.97. PMID: 32395440; PMCID: PMC7192664. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7192664/

• Systematic review and meta-analysis of the efficacy and safety of chromium supplementation in diabetes https://www.researchgate.net/publication/260838498_Systematic_review_and_meta-analysis_of_the_efficacy_and_safety_of_chromium_supplementation_in_diabetes

• Brownley, K. A., Von Holle, A., Hamer, R. M., La Via, M., & Bulik, C. M. (2013). A double-blind, randomized pilot trial of chromium picolinate for binge eating disorder: results of the Binge Eating and Chromium (BEACh) study. Journal of psychosomatic research, 75(1), 36–42.
• Pei D, Hsieh CH, Hung YJ, Li JC, Lee CH, Kuo SW. The influence of chromium chloride-containing milk to glycemic control of patients with type 2 diabetes mellitus: a randomized, double-blind, placebo-controlled trial. Metabolism. 2006 Jul;55(7):923-7.