Multiple regression standardized coef changed direction even with low VIF I have an outcome with predictors a, b, c
The correlations of these variables are 
                 outcome          a            b        c    
outcome          1.0000000     -0.3330094  -0.5882250 -0.2778692
a               -0.3330094      1.0000000   0.4222888  0.7404057
b               -0.5882250      0.4222888   1.0000000  0.7030850
c               -0.2778692      0.7404057   0.7030850  1.0000000

I would have assumed that the coefficients of the standardized variables would have all been negative in multiple regression, but that is not what happened as shown below:
term          estimate  std.error
intercept       0           0.08  
a             -.47          0.13
b             -.86          0.12
c              .61          0.16

To my surprise c was positive. My first thought was to check collinearity with car::vif(). My results were as follows
term    vif
a       2.3
b       2.0
c       3.7

I usually use the rule-of-thumb that a vif of 5 indicates collinearity. In this case I don't see collinearity present. 
How do I explain the change in the sign of term c?
 A: There is not enough information to give a definitive answer, but from the information given, this seems like partial correlation sign reversal and suppression.
In the case presented, multivariate regression has c being positive but a bivariate regression has c being negative - noted in a comment. This is a sign (pardon the pun) of partial correlation sign reversal and suppression.
In addition there is a negative correlation of a, b and c to the outcome, but positive correlation to each other. That is another lead. When combined with the sign reversal between multivariate and bivariate, the evidence becomes strong.
The explanation the OP is asking for, as @whuber pointed out, of the multivariate model is c has a positive effect when taking into account the effects of a and b. a, b and c are working together to explain outcome. But you may want to examine why, understand it and perhaps control for it.
I hate to put in links but without the data, I cannot prove my points.
Here is one page on this site that discusses this issue more in depth.
The wikipedia page gives some tests that may help. 
Andrew Gelman has a post. 
