You need a trimmable stabilizer in two cases:
- In transsonic flight when local shocks render the elevator ineffective, or
- In case of powerful flaps which require a wider trim range than what a regular elevator can provide.
If you can get by with a fixed tailplane, not only the weight saving but also the reduced complexity should be weighed against the increase in efficiency. If your elevator trim deflections in climb and cruise are within single digits, the drag increase is negligible. If you need more trim deflection during approach, the drag increase might even be welcome.
Make sure that with all trim deflections your elevator maintains sufficient control authority. Then a fixed tailplane is the best choice. The weight increase versus efficiency calculation should only decide wether to use a trimmable stabilizer or not if you need to achieve a specific performance figure. Normally, the extended trim range is what is pushing engineers to choose a trimmable stabilizer. If it is not needed, it is better avoided in order to ease maintenance and to avoid the new failure modes which come with more moving parts.