[R] Error distribution question

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Hello there,
I was wondering if somebody could offer me some advice on which error 
distribution would be appropriate for the type of data I have. I'm 
studying what continuous predictor variables such as grooming received, 
rank, etc. affect the amount of grooming given. This response variable 
is continuous with many zeros, and so positively skewed. So I can't use 
gamma because of the zeros and since poisson is for count data I would 
probably loose lots of info when converting my data to integers. I was 
looking in the help archive of R and I realized that somebody had a 
similar problem in the past and was adviced'  to use the Tweedie 
distribution since it was developed specifically for dealing with 
positive continuous data with exact zeros. I think this would be 
appropriate for my problem as well, but I'm not sure. I realized in the 
Tweedie help page that one can use a specific response distribution 
(Normal, Poisson, Compound Poisson, etc) by setting the variance power = 
to a specific number. I'm a beginner, so I really don't follow then, 
which response distribution to use (i.e. what variance power) that would 
be appropriate for continuous response data with many zeros.
I hope somebody can help me with this.
Thanks in advance.
Cheers,
Cristina.