Is weak coffee more likely to be bitter?
It's not so much that weak coffee is bitter, as that over-extracted coffee is bitter. If you want it strong but don't use enough ground coffee, you can get more flavour by leaving the water on the grounds for longer. But then the bitter flavours come out. The opposite is espresso; a decent espresso is of course strong but not at all bitter and extraction is quick. 

Another factor may be that some of the bitter compounds come out early but are masked or made acceptable by the other flavours

Water temperature also plays a role in which components of the flavour are extracted, but I assume that's fixed.