What is the best medicine for bipolar that does not cause weight gain?

Hi, Mellanier!
Many, if not most, antidepressants and antipsychotic medication have the potential to cause weight gain in some people... it depends on how you respond to any given drug. Just because you gain weight on one doesn't necessarily mean you will on a different medication.
Are you taking medications for your Bipolar disorder or just an antidepressant for depression? Bipolar medications include mood stabilizers like lithium and lamotrigine and antipsychotics such as Vraylar, Abilify, and Latuda among others.
If you're just taking an antidepressant bupropion (Wellbutrin) is probably the most weight neutral and safer to use with Bipolar disorder. If you need a medication for Bipolar depression Latuda would be worth a try.
Have you talked to your health care professional about your weight gain and did you discuss your options? If not, that would be a good first step.

Lamotrigine (Lamictal) works well for my bipolar 2 disorder with no weight gain.