What is happening is that the camera doesn't really know that you want to focus on the lizard's eyes so it focuses on where it thinks is best. In this case it looks like it focused on the centre of the image, the lizard's elbow (if its called an elbow). This happened either because it is manually set to choose the centre focus point or else it is the one it happened to chose. If I'm not mistaken when you set the metering to centre weighted it does actually influence the decision on which focus point to use putting more bias towards the centre one.
In any case there are various ways around it, depending on how dynamic the subject is.
1. Set the focus point to manual selection - this way you have a choice of 11 points to focus on which in many cases is enough for one of them to be in the right place. If not just recompose a little until you get one of the points in the right place and then select that point.
2. Keep it manually on the centre point, point the camera at what you want to focus on (the eyes in this case), half press the shuttter to focus and then recompose and shoot. The focus will remain fixed on what it was when you half pressed the shutter. (but make sure the focus mode is AF.S and not AF.C or AF.A). This is good for most instances but has some limitations when shooting macro as when you recompose you might actually move the camera nearer or closer to the subject. This happens even when using a tripod, at least with most types of 'ordinary' tripods. With most tripods the change in distance happens only when you recompose vertically, so you can avoid the problem if you only need to recompose horizontally.
3. For macro shots of subjects that do not stay still for any length of time - including lizards - my preferred method is to move just a little bit further and point the camera right at the point I want to focus on and shoot - then I recompose the photo by cropping. This of course loses some resolution but this is outweighed by the sharper focus obtainable this way. The photo below is taken that way.
4. Yet another way is to use manual focus and the so called 'focus peaking' in live view. This is great because it shows you all in one go all the parts of the image that are in focus by highlighting them with a bright outline. This is instantaneous so you can even use it on moving subjects and snapping as soon as the part you want is in focus. The downside is that focus peaking works only with the LCD on the back which in many situations, especially bright sunlight, can be difficult to see.
5. Another crazy thing that rather unexpectedly works quite often is to use the face recognition mode (only works in live view). I was surprised at in how many bugs, reptiles and other creatures the camera actually recognises as being their face. It is interesting and somewhat amusing to see it recognise a beetle's 'face' but I wouldn't really count on it.
Using the viewfinder to focus manually is not really an option in my opinion as it is not nearly accurate enough - at least not with the stock viewfinder screen.
In this photo I focused on the eye, but the focus turned out to be just a little behind that. That difference is what can be fixed by the focus fine adjustment. When I shot this photo I had not yet calibrated the focus for that particular lens. If I had then I'd have got the eye in perfect focus.