negative weights

Weights in 'nls' and in forecasting are two very different things. 
Weights in functions like 'nls', 'lm', 'lme', and often also 'optim' are 
typically justified from a maximum likelihood argument.  In that case, 
the weights are (exactly or metaphorically, depending on context) 
inversely proportional to the variances of the observations.  Negative 
weights in that context implies imaginary standard deviations;  I'll let 
you extrapolate from there.

	  Weights in forecasting, however, commonly occur when modeling, for 
example, the output of a reactor:  If the reactor delivers less than its 
standard output on one cycle, it will often do the opposite on the next. 
  This is common with straight "moving average" models in the standard 
time series literature, e.g., the famous Box and Jenkins (or Box, 
Jenkins and Reinsel now) book "Time Series Analysis, Forecasting and 
Control".  Any good book on "arima" / "Box Jenkins" modeling should 
discuss this.  You can get started on this with the time series chapter 
in the Venables and Ripley book, "Modern Applied Statistics with S".

	  hope this helps,
	  spencer graves