Answer first: the titration schedule exists to let tolerance to the gastrointestinal effects develop between steps, and every step in it is a tolerability decision rather than an efficacy one.
Liraglutide titrates weekly rather than four-weekly because its half-life is about thirteen hours, so steady state is reached within days. The interval follows the pharmacokinetics in both cases.
More usefully, the dose that produces an acceptable result with acceptable tolerability is the endpoint, not the top of the schedule. A substantial fraction of trial participants did well below the maximum.
Titration schedules in the licensed products were designed specifically to manage gastrointestinal tolerability, and that intent is stated in the clinical development literature.
Nothing here is medical advice, and research-use compounds are not approved for human use.
Four half-lives between steps, minimum. Work it out for your agent.