Even at low doses can benzodiazepines suppress breathing and why could this be as they should relax you?

Suppress CNS: The action of benzodiazepines at the level of the Central Nervous System. Typically, they shouldn't affect respiration function in normal folks at very low doses BUT still they have the potential to affect some people adversely under certain conditions (age, other medications being taken, poor breathing to begin with) and so no matter whether doses are low or otherwise caution is always advised.