Your δx and δy values set how much each point counts in the fit. This choice changes parameter uncertainties, not the fitted parameters. It also changes uncertainty bands and Model Evaluator uncertainties; weights, residuals and χ² are unchanged.

Absolute treats your values as true 1σ measurement errors, such as calibrated instrument specifications. Parameter uncertainties follow from them directly, so scatter beyond those errors does not enlarge them. A χ²_red well above 1 then suggests missing error sources or an unsuitable model.

Nominal (the default, and curve.fit’s original behavior) trusts only their relative sizes, as when the overall error scale is unknown, and estimates the overall scale from the residual scatter, multiplying parameter uncertainties by . This assumes the model is correct. When χ²_red ≈ 1, both agree.

SciPy (curve_fit, ODR), lmfit, Origin and Mathematica scale like Nominal by default; IGOR Pro and Astropy treat supplied uncertainties as Absolute. Absolute needs Table or Expression uncertainties. More in Help.