Why does thallium form TlF and TlF3 but aluminium only forms AlF3?
Ahh, Thallium is a very nice element. Because it's weird.

The +3 oxidation states are favorable except for the heavier elements, such as Tl, which prefer the +1 oxidation state due to its stability; this is known as the inert pair effect. Chemwiki.UCDavis
As an example in group 13 the +1 oxidation state of Tl is the most stable and Tl(III) compounds are comparatively rare. Inert pair effect, Wikipedia

So, why?
Inert pair effect was introduced to describe why the facts above are correct. However, the original explanation, provided by Sidgwick, relied on the fact that the $s$ subshell has an &quot;inert&quot; pair of electrons. This can't be correct, and Wikipedia uses the trend in ionization potentials of &quot;$s$&quot; electrons to prove it wrong:
$$\ce{In &lt; Al &lt; Tl &lt; Ga}$$
A better explanation lies within the lower bond enthalpies of $\ce{MX}$ where M is one of the p-block heavy elements.
To reach a high oxidation number, elements will need to have a strong bond. They wanna bond in order to lose energy (i.e. become more stable) after all! If the bond is weak, this energy isn't provided. Thus, a heavy element is better off with being less oxidised.
See this and this. (Sorry, they might be behind a paywall)