Herbarium records provide comprehensive information on plant distribution, offering opportunities to construct invasion curves of introduced species, estimate their rates and patterns of expansions in novel ranges, as well as identifying lag times and hence “sleeper weeds”, if any. Lag times especially have rarely been determined for many introduced species, including weeds in the State of Queensland, Australia as the trait is thought to be unpredictable and cannot be screened for. Using herbarium records (1850–2010), we generated various invasiveness indices, and developed simple invasion and standardised proportion curves of changes in distribution with time for ~ 100 established and emerging weed species of Queensland. Four major periods (decades) of increased weed spread (spikes) were identified: 1850s, 1900–1920, 1950–1960 and 2000–2010, especially for grasses and trees/shrubs. Many weeds with spikes in spread periods did so only 1–2 decadal times, except for a few species with higher spike frequencies > 6; the majority of these spikes occurred recently (1950–1990). A significant proportion (~ 60%) of Queensland’s weeds exhibit non-linear increase in spread with time, and hence have lag phases (mean: 45.9 years; range: 12–126 years); of these lag-phase species, 39% are “sleeper” weeds with > 50 years of lag time (mainly trees/shrubs and grasses). Twelve traits of invasiveness, including lag time and species-specific/historical factors were screened, of which frequency of invasion waves, spread rates and residence time were the main drivers of weeds’ distribution. The low predictive power of lag time on weed distribution suggests that retrospective analyses offer little hope for a robust generalisation to identify weeds of tomorrow.