Accepted answer
twelve weeks at 12.5 mg is 84 days at one dose level — and the arithmetic the question hides is that it also moves every dose above 12.5 mg back by 84 days. Whether that reduces headache depends on which quantity it tracks. A symptom driven by the dose itself is unchanged by waiting: 12.5 mg is 12.5 mg on day 1 and on day 84. A symptom driven by the rate of change has 84 days of no change to settle in, which is the case the hold is actually made for. The distinction is testable on your own record: plot headache against days-since-last-increase rather than against dose, and if the peaks line up with the increases the hold is doing something. Escalation schedules are set by a prescriber, and nothing here is medical advice.
Stated carefully, the initiation step in most schedules is not intended to be therapeutic; it is there to introduce the receptor to the drug.
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.
Worth being precise here: 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.
Four to five half-lives to steady state is standard first-order pharmacokinetics and gives the four-week interval directly from the one-week half-life.
Faster titration does not reach the destination sooner in any way that matters; it reaches the symptoms sooner.
Hold rather than escalate while symptoms are active. Always.