I'll give a brief overview of what I saw, and what I think that you can improve upon.
1. XP Dance ASAP in Discovery. You kept it on fertility dance for about half of discovery while getting the extra XP is much better for Aztec's early game.
2. 3 villagers>3 fishing boats. The only civ where this is an exception is Japan on water. Otherwise 3 villagers is just so much better.
3. Constant villager production. One thing that many players near your level sometimes struggle with is constant villager production. Any time you have a spare second hit T+V for get another villy coming. There were a few times when you went for quite some time with no villager training. This is a crucial step to growing as a player.
4. Market! You need one. Get the upgrades as well. This along with #3 are the 2 biggest things in my mind that separate captains and 1st/2nd lts.
5. Eco balance. Your economy was a bit out of wack at several times during the game. Around 7 minutes or so you had something like 700 food and 50 wood, as well as being housed (which will lead into point 6). Try to get your early eco balanced by watching recs and using other peoples BOs.
6. Housing. Try not to get housed early on. It halts villager production, army production, etc. The biggest thing that gave you trouble was eco balance (#5) and lining up shipments (i.e. having both 6 puma/10 mace both waiting to be sent at the same time).
7. A quick note on your deck. I think that for Aztec (any almost any civ for this matter) you need to have 700 wood and 600 coin. 700 wood just because its such an insane card (I probably send it as my first age 2 card in like 80% of my games) and 600 coin for when you need to age. This is just an opinion of mine and ofc you are free to do as you wish with your deck. I noticed you had 3 TP travois as well as both schooner shipments in your deck. You probably wont need to boom quite that hard, you might consider removing one or the other, or having multiple decks (one for TPs, one for sea boom).
8. Don't ship 4 canoes when you did. I would only ship it as a last resort with native civs. Especially no need for it when he shows no signs of wanting to touch your water.
9. Don't use attack dance when you aren't fighting. At times you had attack dance going when you were just sitting back and massing/booming/aging. Switch it to the WP dance and grab some of them while you have the chance.
10. Pressure!!!!! I can't stress how important it is to maintain proper pressure. Especially with a civ like Aztec, where games are literally won and lost based on how well you can harass/pressure.
11. Upgrade all your units when you age. You had the resources, you just didn't do it.
Hope this helps a bit. Feel free to add me on ESO: Zutazuta.