There are a few studies that describe the impact of obesity on the pharmacokinetic profiles of immunosuppression.
A particularly good review is this one:
Campara M, Lourenco LM, Melaragno JI, Kaiser TE. Implications for body weight extremes in solid organ transplantation. Pharmacotherapy. 2021 Jan;41(1):44-58. doi: 10.1002/phar.2493. Epub 2021 Jan 19. PMID: 33301647.
They note that induction immunosuppression does not appear to be significantly impacted by adiposity. They do note however that with rATG dosing being weight based, that there are concerns for underdosing in obese patients. They mention that using CD3 counts i.e. confirming depletion is a reasonable way to titrate dosing.
Maintenance immunosuppression wise, there appears to be an association of higher BMI and increased tacrolimus levels. Mycophenolate was less clear and belatacept is similar to monoclonal/polyclonal antibody induction. The authors do a nice job of mentioning significant limitations/caveats to many of these studies including BMI as a measure of adiposity, racial differences, genetic differences.
They include an excellent table, Table 4, that summarizes how best to titrate medications based on BMI.