The movie Prometheus and Alien android designs:

Question

Why are the androids in ALIENS and ALIEN³ designed after the original Weyland from AVP, but not in any of the other movies?

Answer 1

First of all, the main point to consider is that the Alien (and later Alien/Predator) universe is not an entirely pre-thought and consistently grown universe, with the stories well tied into each other. There were different producers, directors and story-tellers taking turns on the story and including additional stuff (like the merge with the Predator-franchise). And with the resulting advantage of a conglomerate of entirely different genres and styles comes the disadvantage of sacrificing some coherence and overall consistency of the story. Rather than continuing some established universe, future sequels rather took their pick at interpreting and contuing the story, referencing previous events and characters as they see fit (or not at all), neccessarily introducing some problems with previous story aspects in the course. But we might be able to provide a little rundown of how the character of Weyland and the androids developed in the movies:

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The first Alien movie did likely not have any future sequels in mind right from the start, let alone the appearance of the original creator of the androids and the fact of them being modeled after him. Those androids were just modeled in some varied way (as the crew of the Nostromo also didn't know about Ash being an android at all). Thus this aspect was just not thought about yet. Then in Aliens the role of the synthetic human was played by Lance Henriksen. I think also at this point there was likely not yet a consideration of the androids being modeled after any real life person, but just in a normal diversified way.

Then at the end of Alien³ we have Lance Henriksen play the head of the Weyland company. But it seems that was rather introduced into the story as a reminiscence (for both Ripley and the audience) to the original Bishop, chosen for Ripley to better draw a connection to someone she already had a connection to (in the same way as the T-800 was selected to kill John Connor due to his previous relationship with him, to draw a connection to an entirely different movie franchise). It is IMHO not clear if this was really the head of the Weyland company (as he stated, I think) or just another of those androids modeled after the original Weyland and just claiming to be him (though, IMDb lists him as "Bishop II"). But disregarding if the role from Alien³ was really supposed to be Weyland or not, the fact that the androids were modeled after the original Weyland was not introduced, let alone thought about, before the creation of the story for Alien³ and the fact that not neccessarily all of the androids were modeled after him (be it in past movies, or also in Alien: Resurrection) was just a minor inconsistency to be accepted, or rather a coincidence for Ripley to stumble across one of the "Weyland-style" models.

Then there came the merge of franchises with AVP: Aliens vs. Predator. This built upon the previously introduced fact of at least Bishop being modeled after Weyland and used this to make Lance Henriksen reprise the role of the original Weyland in the present (our present, when AVP is set). But this was IMHO rather made as a neat reference to the previous movies than to really strengthen the fact of all androids being built after Weyland.

Then there is also the newest installment of Prometheus which was itself made as a (maybe/maybe not) prequel to the first Alien movie and Ridley Scott has clarified that it is not related to any of the following movies (or at least any of the AVP movies) in any way. So there isn't any connection of Prometheus' Weyland to his depictions in the previous movies, let alone the fact of him modeling his androids after his likeness.

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So to sum up, the out-of-universe answer is that this aspect wasn't thought out right from the beginning and this is just one of those little inconsistencies resulting from the heterogenous nature of the Aliens/Predator universe. If you would like to have some possible in-universe reason, then it might very well be that not all of the androids were modeled after Charles Bishop Weyland or his descendants, but only some of them.

Answer 2

I believe Lance Henriksen assumed the role of android in Aliens and did a character as Weyland in AVP. Aliens and Alien vs predator universe are not related by any means.