This response addresses concerns with collinearity when the goal is description and inference, not prediction.
In linear models, some level of collinearity will always be present in data where the presence of strong collinearity suggests predictors that are redundant with one another. It then becomes a matter of choice as to which predictors to retain and which to eliminate as useless, uninformative or less informative. At that point the questions are: how much collinearity can be present before a regression model's performance degrades? What are some approaches to managing the problem?
Usually this isn't a simple, one-step solution. Rather, it's step-by-step.
Cookbook rules-of-thumb for VIFs abound but the goal is always to minimize the risk of model degradation from collinearity. One prescription is for absolute VIF values around 5 where VIFs greater than 5 are considered problematic and VIFs less than five acceptable or normal (different sources prescribe different cut-offs).
Since collinearity is a function of undesirable dependence among predictors, analyzing a matrix of pairwise Pearson correlations is not only not helpful, it can actually be misleading. First, the correlations are pairwise. This means they don't reflect association with other predictors. Moreover, the magnitude of the correlations is not a useful diagnostic wrt any actual underlying collinearity as lower valued correlations can be collinear while big magnitude correlations may not be.
A better first step would be exploratory: start with a matrix of pairwise correlations and scatterplots between the dependent variable and the predictors, taken one at a time. This is useful in identifying predictors that have little or no association with the DV. Chances are that if they can't be transformed into useful predictors, then they can be eliminated as uninformative. Retain both the magnitude and sign (pos./neg.) of these DV-predictor correlations as these metrics can be useful in later steps.
Assuming you have identified a reduced set of variates, a much better diagnostic than pairwise correlations would be to examine a matrix of partial correlations (excluding the dependent variable). You are looking for high magnitude, absolute valued partials. This should target problematic, pairwise dependence between predictors.
Factor analysis with rotation can also be useful. First, standardize the variables (again, excluding the dependent variable) to a mean of 0 and std deviation of 1 and then run a factor analysis with rotation. Based on the factor loadings you will gain insight into dependence among predictors. Some analysts even use the factor loadings as a decision tool wrt variates to retain vs eliminate. Simply retain those variables with the highest loadings on each factor and throw away the rest. (Note that throwing away potentially useful variables that are not top-loading can be wasteful.)
Having a reduced set of variates does not mean that collinearity has been eliminated. The next step is to run the regression on this reduced set being sure to include coefficients, std errors, t-values along with VIFs, tolerances, etc., as you have reported in your post. The VIF values will have changed relative to those reported in your original post above.
So, having identified a set of problematic variables based on their partial correlations, a factor analysis and/or the new VIFs, the issue becomes one of managing the collinearity. Again, this isn't a simple, one-step process. In doing so you don't want to be too clinical and reduce collinearity down to zero.
Start with the largest magnitude VIF. Identify that variate's collinear predictor (VIFs are uninformative about this) based on the diagnostics from the partials or factor structure and, based on the results of the regression, look at the coefficients and absolute t-values for this pair. Usually one of the coefficients is wrong-signed wrt the original correlation between the DV and predictors (from the step above). In addition, the absolute t-value for this wrong-signed predictor is usually smaller. At this point it's a safe decision to eliminate this wrong-signed, smaller t-value predictor and retain the correctly signed predictor.
Rerun the regression on this new set of reduced variates, repeating the inspection for the next largest pair of VIFs. Iterate until the metrics reach a level of collinearity you are comfortable with, e.g., reduced models with VIFs around some preferred cutoff or threshold. Always bear in mind that cookbook rules such as VIF cut-offs can be bent, if not broken.
In this way you should be able to build a reduced model that minimizes any risk of degradation as a function of collinearity.