Weaver has joined the Clarets after a spell with Scottish Premier League side Dundee United.
The 30-year-old, who has also played for Charlton, will be available to face Chelsea on Saturday, subject to international clearance.
Safe hands: Nicky Weaver has joined Burnley for six months
Laws is now determined to make further additions to his squad before the window slams shut next week.
The new boss believes he is short on numbers as the club battle to beat the drop and is understood to be keen on Celtic left back Danny Fox and Stoke defender Leon Cort.
After losing his first three games in charge, Laws said: 'The one thing the players need is support. We haven't got the biggest squad in the world and when you lose good players it affects your team.'
Laws expects to call on defender Andre Bikey for the home match against Chelsea on Saturday.
It is a welcome boost for Laws as influential skipper Graham Alexander (calf) and Chris McCann (knee) were both injured in the first 15 minutes against a Bolton side managed by former Clarets boss Owen Coyle.
Timely return: Andre Bikey (centre) has been away on international duty
So the return of the versatile Bikey, who has been on African Nations Cup duty for Cameroon, could not be more timely.
Laws said: 'We are due to assess the injuries to Graham and Chris. But the good thing is we have got Andre back from international duty, so that is a plus.
'I spoke to him on the phone, so we know he will be here for the weekend. That is great news because we need all the quality we can at this time.'
Burnley have now taken only one point out of a possible 36 on the road and Laws knows that is relegation form.
He added: 'There is nobody more aware of how tough a job this is than me. But we have come in here believing we can keep the club in the Premier League and that's what we will do.'
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