Hello~In general, no, they are not like synthetic, in fact, they may actually help in loosing weight naturally as they match your body's metabolism therefore working together with it.
However, this being said, you will read many pros and cons regarding this. If they did cause weight gain or other side effects, it would be due to the estrogen, if you are "estrogen dominant" then possibly that hormone could cause some weight gain, but taking it with bio-identical progesterone would help with that side effect.
Here is a web site from the pioneer in bio-identical hormones, Dr. John Lee. He mainly talks about Progesterone, but he also covers the others as well. https://www.johnleemd.com/
Another good resource is Dr Christine Northrup, here is her site: https://www.drnorthrup.com/tag/bioidentical-hormones/
I hope this helps.
I think it is important to understand that bioidentical hormones are still synthetically made often. They often come from yams and soy and are supposed to be 'identical' to hormones we make. But they are still synthetically driven. This article was really helpful for me to understand bioidenticals. It does state that no one really knows if they are safer than other types of hormones. https://www.health.harvard.edu/womens-health/what-are-bioidentical-hormones I believe the stance by medical professionals is that more research is needed.
As to gaining weight when taking them, we are all individual and have our own unique response. Some women lose weight and some gain weight.