Second-harmonic generation (SHG) is a fundamental tool in modern laser technology, enabling coherent frequency conversion to remote optical bands, serving as the basis for self-referenced femtosecond lasers and quadrature-squeezed light sources. State-of-the-art SHG relies on bulk crystals and ridge waveguides, although continuous-wave (CW) SH efficiency in bulk crystals is limited by short interaction lengths and large mode areas. Ridge waveguides offer better performance with lower pump power requirements, yet must span several centimeters to deliver high output power, complicating fabrication and narrowing the bandwidth. Recently, SHG in periodically poled thin-film lithium niobate integrated photonic circuits has attracted significant interest, offering orders-of-magnitude improvement in SHG under CW pumping due to the stronger optical mode confinement. However, lithium niobate has a low optical damage threshold, even in MgO-doped substrates, which limits SH power output to well below the watt level. Here, we overcome this challenge and demonstrate 7 mm-long periodically poled thin-film lithium tantalate (PPLT) waveguides that achieve high SH output in the CW regime, with generated power exceeding 1 W and off-chip output above 0.5 W at 775 nm under 4.5 W pump power. PPLT offers a higher optical damage threshold than PPLN and supports watt-level operation. By optimizing electrode geometry and poling conditions, we obtain reproducible poling despite lithium tantalate's coercive field being nearly four times higher than that of MgO-doped lithium niobate. Although its effective nonlinearity is more than five times lower, we achieve watt-level CW output with a short waveguide, demonstrating the potential of PPLT circuits for high-power applications in integrated lasers, quantum photonics, AMO physics, optical clocks, and frequency metrology.