Need help choosing a new lens for my Canon 1200d

Small/lightweight, easily affordable and excellent quality just isn't really a combination that exists, unfortunately! Or if it does, noone has been able to find or build it! 

The 75-300mm lens which came with your 1200D is not a stellar lens, it's true. There are better zoom lenses which cover the 70-300mm range which are under the $1000 mark. Canon makes one or two (I'm a Nikon shooter so I'm not so familiar with them), and also an "L" series 70-300 which will be much more expensive. Tamron and Sigma will also have affordable options for this focal length range which are reasonably well regarded. These will only go so far towards improving upon the results of the 75-300, however. For birds, you usually want a longer range lens so you don't have to crop so much...

Your budget would get you close to a Sigma 150-600 or Tamron 150-600 which will give you much more zoom range and stop you needing to crop so much... but they are over the $1000 mark when purchased new, and they are large and about 2kg in weight. I have gone for long walks/hikes with the Tamron but it's quite a burden to bear. Too heavy for the camera strap, too, so you'll want an over-the-shoulder type strap like those made by Black Rapid which attach directly to the lens. There are also older, cheaper options like the Sigma 150-500mm and 50-500mm lenses which you might be able to find on the used market. These will dwarf your current lens, however.

On many of the above options, there will be options for lenses with and without image stabilisation (also called vibration reduction, vibration control, optical stabilisation by the various manufacturers). The longer telephoto lenses benefit greatly from this feature, as it helps counteract the natural wobble of your hands. I'd strongly recommend it in any of the lenses above, so research carefully. Lenses which lack it will be cheaper, but are generally older or of lesser quality and will be harder to use.

Canon do make a lens which is the envy of many Nikon (and other brand) shooters in the form of the 400mm f/5.6 prime. This is a fixed focal length lens which you can't zoom in and out, and which lacks image stabilisation. It's also fairly large and quite expensive (~$1700 new). This is probably the best option, but it's serious overkill for a hobby shooter and certainly overkill on an entry level body like the 1200D. 

shorty makes good sense - the more you practice and use your camera gear, the more you'll understand and appreciate its limitations and learn how to get the best out of it, which will help you make an informed decision. You may start to appreciate the reasons why better gear becomes bigger, pricier etc, and opt to upgrade, or you may not. Consider looking at used items, but obviously this will come with its own risks.