Here is my Weyland Corp deck that I made from my available card pool. Right now I only have the Core set and Trace Amount expansion. Within the upcoming week I will have a 2nd Core set and Cyber Exodus so let me know if you think any cards will help feel free to make the recommendations.
3 Priority Requisition
3 Executive Retreat
3 Hostile Takeover
3 Ice Wall
2 Hadrian's Wall
2 Heimdall 1.0
3 Data Raven
2 Amazon Industrial Zone
3 Pad Campaign
Melange Mining Core
3 Hedge Fund
3 Beanstalk Royalties
2 Scorched Earth
2 Shipment from Kaguya
2 Power Grid Overload
there it is, let me know what you all think.
1) Project Atlas is the best agenda in the game right now. Running fewer than three in Weyland is a mistake.
2) You have 19 pieces of ICE, which is reasonable, but is a little lighter than I like to run. I don't understand all your "two of" ICE, though. With something like ICE, I either want to draw it consistently, or I don't include it. Remember that by the late game you are probably throwing away a lot of the ICE you draw anyway. The numbers are all about how quickly you find particular pieces. Think hard about what you are really hoping to draw and maximise that (subject to influence).
3) Research Station is currently bad. It will probably remain bad for a long time, since the runner can trash it very easily on a run they probably want to make any way.
4) One Malenge is a waste. You can't reliably find it, and your only copy may well get trashed before you can play it. Drop this for something else (such as a second Security Subcontract, which combos well with Amazon Industrial Zone, and is harder to trash.
5) Shipment from Kaguya only really fits in decks designed to abuse advancement. This is not one of those decks.
6) I don't like Power Grid Overload. Or the single Ghost Branch.
Overall, I think your deck lacks focus. It really has that "thrown together" feel that loads of singletons and doubles tends to indicate. What you want is a more specific plan which your deck is optimised to hit. Because you are going in so many directions at once, it's hard to offer you advice, because focusing more on direction A means dropping direction B, C and D, and ultimately only you can decide what you want to focus on.
Here's an example, off the top of my head. Suppose I want to focus on high trash assets that provide me with a steady income (or break the runner's bank trying to stop me - obvious weakness to Wizzard is obvious, but probably safe). I'd start this deck with three Amazon Industrial Zone and three Security Subcontract, as well as my agendas. I'd then find 20 ICE from Weyland or Neutral factions, and throw in the standard economy cards (with PAD being chosen over Melange). Note that I've not spent any influence at this point, and already have a rough deck.
I would then look to see how influence could improve this deck. One obvious card is the Jenteki Sysop who reduces res costs, as this fits with the rest of my engine. Of course, Adonis also fits the high trash passive income model. I probably don't care too much about OOF ICE, but perhaps a Rototurret or the like would help keep the Runner honest. Another option would be SanSan, which fits with the high trash asset theme, and gives you a fast advance option once you have your economy up and running.
From there, playtesting sanity checks my ICE choices and influence spending. I might find that I already have enough income that I don't need Adonis, and that SanSan really helps against Big Rig Shaper in the late game. Or I might find that three Hostile Takeover are not enough to properly support Archer, and so I throw in some more Posted Bounty.
This looks nothing like what I actually play, of course, but it's not too far from what you posted, only far more optimised for one particular line of attack.