Beta Coefficient range? Is there a table of range for beta coefficients used in multiple linear regression that we can use to interpret if influence is strong, very strong, weak or very weak.
 A: Not directly, it would seem. However, it is these very moments where we would do well to consult with our dear friend Keith. 
He advises:

However, if you're like me, you'll still want something reminiscent of Cohen's d, along with a rule of thumb for determining small, medium and large effect sizes. Later he adds:

Keith is such an accommodating fellow that he includes the formulae for calculating Cohen's f2 from R2 and change in R2: 


Alternatively, you could try this effect size calculator.
Despite these recommended effect sizes, however, it's important to note that effect sizes are very much dependent upon the discipline in question.
References
1: Keith, T. Z. (2014). Multiple regression and beyond: An introduction to multiple regression and structural equation modeling. Routledge.
A: The estimated $\hat\beta$ will range differently depending on your data (depending on both $X$ and $Y$)!
So no, there is no table... 
But if you do the regression on standardized variables (zero mean, unit variance), then your coefficients will also be standardized: each $\beta$ will belongs to $[-1,1]$ and will reflect their influence on your dependent variables a bit like a correlation coefficient does. Namely you get the direction of influence in the sign of the standardized $\beta$ and their strength in their magnitude in a standardize fashion (namely a magnitude from 0 to 1).
Moreover you can evaluate how significant each of these coefficients are, by computing their statistics, as shown below.

EDIT: (Below, my old answer that was not exactly about the influence of the coefficients but more on their statistical significance)
However if you used classic least-square to solve the linear regression, under classic assumptions (resiudals normally distributed), you can find statistics for the $\hat\beta$, then p-values, and confidence interval come along.
Namely, for $n$ data points, in the case of a simple linear regression (univariate, scalar dependent variable) the standard errors are:
$$
s^2 = \frac{\sum_{i=1}^{n} (y_i - \hat y_i)^2}{n-2}
$$
$$
SE(\hat\beta_0) = s\sqrt{\frac{\sum_{i=1}^{n} x_i^2}{n\sum_{i=1}^{n} x_i^2-(\sum_{i=1}^{n} x_i)^2}}
$$
$$
SE(\hat\beta_1) = s\sqrt{\frac{n}{n\sum_{i=1}^{n} x_i^2-(\sum_{i=1}^{n} x_i)^2}}
$$
where $s^2$ is the sample variance of $y$. Now each standard error will help you compute the t-statistics and get p-values for testing the hypothesis of having a $\beta \neq 0$ (the normalized t-statistics for e.g. $\hat\beta_1$: $t_{\hat\beta_1} = \frac{\hat\beta_1}{SE(\hat\beta_1)}$ follows a t-distribution with $n-2$ degrees of freedom). 
For multiple regression (so dealing with data matrix $X$ and $Y$), you can read the standard errors of each $\beta$ by taking the square root of the diagonal elements of the variance covariance matrix of the joint distribution of all $\hat\beta$s:
$$
s^2(X^TX)^{-1}
$$
See this book chapter for better and detailed explanations.
A: I believe the values posted by JPMD are comparable with Cohen's recommendations for the Pearson correlation coefficient r rather than d, which is a completely different statistic (where Cohen's recommendations for small/medium/large were 0.3/0.5/0.8).  However I assume they would also apply to other measures of association constrained to the range -1 to +1 such as R, and maybe also standardised regression coefficients which is what this thread is about.
Even though Cohen was a psychologist, my impression of the conventional interpretation of correlations in psychology (my field) is that 0.1 is trivial, ~0.3 is small, ~0.5 is medium, and >0.6 is large.
A: For simple regression $\beta$ is like R. 
Thus I would use R rules of thumb...
I use the follwoing with my Psychology students:


*

*$\beta$ < 0.1 - Small effect size

*$\beta \in $ [0.1; 0.5[ - Medium effect size

*$\beta \geq $  0.5 - Large effect size


For multiple regression these rules are not that straightfoward, but for Social Sciences they seem to hold (also following Cohen's d suggestions).
