Interpretation very small standardized coefficient beta In one of my studies I have results similar to the below:
β=-0.0007 (95% CI: -0.0009, -0.0002), p=0.01
Since β is so small (but also the Confidence Interval (CI)), is this result still meaningful? 
I don't want to be blinded by a significant p-value.
Note: the outcome measures from which this is derived are all small (0.55; 0.56; etc). 
 A: You should have a look at the concept of statistical / practical significance. This is especially true if you have large sample sizes, as most standard statistical tests are not really designed for such cases, that is most tests will find a statistical significant result simply because of the mass of data.
Your results are statistically significant, however they do also look practically insignificant based on the CI. Whether they are or not is something that you have to decide using your domain knowledge on the subject.
A: If the outcome measure is in the region of 0.55 as stated in the OP, then the regression coefficient $\beta$ has the interpretation that a 1 unit change in the  variable to which $\beta$ applies is associated with a -0.0007 x 0.55 = -0.000385 unit change in the outcome. If this change (0.000385 on whatever scale the outcome is measured) has any practical significance, then yes, it is meaningful. If 0.000385 is of no practical significance then it is not meaningful.
Statistical significance in no way implies practical significance.
Consider a hypothetical study that investigates an intervention designed to reduce BMI in overweight participants over a 2 year period. Say that the coefficient for the treatment effect is 0.5 and highly significant. Over a 2-year period this may be considered practically insignificant, but over a period of 2 months it might be considered highly practically significant.
Context is extremely important in assessing practical significance and can only be evaluated well by using expert/clinical/domain knowledge.
