If there is a high level of spatial homogeneity in your data, you can have multicolinearity within a single variable. Since GWR is, in effect, a local moving window regression, the multicolinearity issue is in regard to redundant values within a local fit and not between variables. The term multicollinearty is very misleading and not consistent with the traditional statistical usage of the term, I wish ESRI would quit using it. I imagine that the returned error is correct and is indicating that you have so much redundancy within some local scale that GWR cannot fit the model.
However, I have no idea why converting to an integer would allow the model to run, it should work the other way because floating point values would provide additional variability. This seems like a fairly serious flaw in the ESRI implementation of GWR. One possibility is that the integer values are being treated explicitly as factorial values and the code is allowing fit for very few nominal levels whereas the error check in the code is not allowing a fit of the same unique number of values when continuous.
This is a good example on why statistical analysis should not be performed in ArcGIS. You have no tools for exploratory data analysis, which should be performed before specifying a model. Are you sure that you even have nonstationarity present in the data? If not, then a GWR is not an appropriate model and you should fall back on more standard regression techniques (eg., GLM, OLS, mixed effect models).
Some summary statistics and a general idea of the spatial structure of your data would go a long way in helping us understand what may be going on here. Questions along the lines of "I received this error, why?" normally do not yield satisfactory answers. Even in this case, I am simply speculating on some possible causes. More information, hopefully to the point of a repeatable problem, is what you should be aiming for in a well formulated question.