The FCC requires that airborne transmitters identify themselves by broadcasting the an FAA designator such as the aircraft registration number.[1] The FAA has no identification or registration process for small weather balloons. So this effectively prohibits them from broadcasting. It's possible to add a radar reflector, but they add significant weight and bulk to the balloon's payload. I think reflectors are only required for larger weather balloons.
1. See § 87.107: https://www.govinfo.gov/content/pkg/CFR-2024-title47-vol5/pd...