Just so happens I researched this myself for a project recently.
So, not really. I mean, there do exist lithium cells in the same form factor as AA and AAA batteries (called a 14500), but there are a few issues. Firstly, the chemistry of a lithium ion cell makes it 3.7v rather than the 1.5v of an alkaline cell or the 1.3v of a Ni-NH cell. So, if you were to use them you'd likely damage your electronics depending on what sort of voltage regulation they use. Secondly, if you overcharge, undercharge, or overheat a lithium cell, they tend to become damaged or combust spectacularly (ie: Galaxy note 7). I think that the big battery manufacturers won't release consumer Li rechargeables due to the liability of someone sticking one in a Ni-MH charger and burning their house down, or sticking them in some piece of electronics and frying it. (They do sell them wholesale for use in battery packs for power tools etc.) So, a few companies have come up with a solution which is to use a smaller lithium cell and embed charging and voltage protection circuitry inside of the AA or AAA form factor itself (link below as an example). However, since only half of the size is the lithium cell itself, the capacity tends to be half of a decent quality Ni-MH which essentially makes it useless unless you want to take advantage of Li's high current capabilities with a very small capacity.
So basically, the available options are as follows. mah listed at a low load scenario:
Non-rechargeable Li AA - 3000mah 15g
Standard AA - 2300mah 24g
Eneloop AA - 1950mah 30g
Eneloop Pro AA - 2550mah 30g
Lithium rechargeable AA - 1040mah 24g
Non-rechargeable Li AAA - 1300mah 7.5g
Standard AAA - 1000mah 11g
Eneloop AAA - 800mah 13g
Eneloop Pro AAA - 950mah 13g
Lithium rechargeable AAA - 450mah 17g
If you want to run AAAs in an AA receptacle, you can use tinfoil or tape like you say as the length is identical, just a different diameter. As a more elegant solution you can purchase or 3d print a set of adapters. An AAA to AA adapter printed in PLA plastic weighs in at 2.8g per battery.
Rechargeable Li AA -
https://www.amazon.ca/Pilot-Automot...9719&sr=1-19&keywords=lithium+AA+rechargeable
AAA to AA 3d printable adapters -
https://www.thingiverse.com/thing:946773
So capacity per weight, the non-rechargeable Li AAs are the winners, and at $15/8-pack aren't too crazy expensive unless your mouse burns through batteries quickly. If you want to shave off another 10g, then the Li AAAs with an adapter are the lightest, but are more expensive than the AAs for less than half the life. The overall cost of Eneloop or similar Ni-MH will depend on whether you already have a charger or not.