You can look into the formalism of Failure Mode and Effects analysis (FMEA) Approach used in Six sigma studies, here, every failure mode under consideration is weighed based on two aspects, one is the probability or frequency of its occurence and two, the significance of the failure mode in terms of the magnitude of the effect it brings to the associated system.

I do not know what are your criteria and sub-criteria, but I guess you can use Analytical Hierarchy Process (AHP) to weight your criteria. You can find a wealth of literature about the method and its application on the internet.

PCA can be a good approach to evaluate weightage for each indicator

I think using an ordination approach such as Principal Component Analysis (PCA) could be a possibility, if you have data on several cases for each element. If you give a bit more information on the objective of the exercise and give examples of what the elements and indicators are, I can give further advice on using this approach or other similar techniques.

Let me add something rather practical and, perhaps one could say, rather unscientific. First, produce a list of the criteria which you wish to consider using (let's say you have 8 potential criteria, but it could be any number). Second, produce a list of people who have (at least some) experience of evaluating wildlife rescue centres (this is the 'expert list', and it should be as long as possible). Third, ask the people on your expert list to rank the criteria from 8 (the most important) to 1 (the least important); people can rank criteria equally if they wish, so that if there are two top ones they would be ranked 7.5, i.e. the average of the two ranks 7 and 8. Finally, calculate the average score for each of the 8 criteria.

These could be your weights, based on what would be termed 'expert judgement'. You may prefer to use the actual numbers which you have calculated, or you may prefer to group them, so that you have, say, one or two important criteria which have a large weight, some possibly less important criteria which you give less weight to, and maybe a criterion or two which had such a small average score that you can reject it (them). Note that this is very approximate, but it gives you an idea of what experts in this area actually feel about the criteria which you plan to use.

A research student of mine used a similar approach in order to understand the importance of various criteria in evaluating sites of potential wildlife conservation importance. This was published in the Journal of Environmental Management, volume 18, pages 153-168, in 1984.